YahooGroups Shutdown
In hopes this will be helpful, I've made a list of alternatives for YahooGroups. I'm making a new post instead of a comment so as to TRY to reduce the overload on 
morgandawn
Groups.io
Only viable option for transfer, but Adult Content not permitted.
Easy import of YahooGroups, but requires Premium Membership for one year $110 $220. https://groups.io/static/pricing
For some reason, they require login to view the process, so I'm pasting it here:
Due to the pending discontinuation of many parts of Yahoo Groups, we ask that all transfer requests be given the go ahead no later than December 1, 2019. We will not be able to guarantee any transfers submitted after that. Also note that it appears that most Photos sections are currently having an outage and it isn't known if they'll be restored prior to the deadline.
Easy Yahoo Group Transfer
Have a Yahoo Group that you want to transfer to Groups.io? We've made the process easy. Please read all of the following, as some of it has changed.
What We Transfer
We can transfer members, archives (without attachments, however), photos, files, links and databases. Calendar entries are not copied at this time.
Premium Group Required
For the transfer, we ask that you sign up for the Premium Yearly plan (you can downgrade to free after a year if you wish).
Steps To Transfer Your Group
These steps must be done in this order otherwise the group transfer process will not happen.
1 Create your new Groups.io group and upgrade it to premium for a year.
2 Set up and start the transfer process by clicking the Set Up New Transfer button, below. You'll be asked to select your Groups.io group and for the name of your Yahoo Group.
3 Send an invite from your Yahoo Group to transfer@groups.io
4 We will accept the invite and then send you an email directing you to make the transfer@groups.io member a moderator.
5 After you have made the transfer@groups.io member a moderator, return here, select your Existing Transfer transfer, and tell us that you are ready for the transfer to happen. Your group must be signed up for the Premium Yearly plan.
6 Once we receive the go ahead, as soon as we are able, we will download the member list and other parts of your Yahoo Group and directly add your members to your new Groups.io group.
Notes
We do not make any changes to your Yahoo Group. We simply make a copy of everything.
We will add all members that are currently confirmed and not bouncing to your group. Members' subscription preferences (email, no email, digest, etc.) will be preserved. Members' posting privileges (group default, override - moderated, etc.) will also be preserved. However, moderator and co-owner status will not be preserved, so all moderators will need to be reinstated after the transfer. If someone is already a member of your new group, we will not change anything about their subscription.
Unless you specify otherwise, we will send a notice to every member telling them about the transfer.
If you have created a customized welcome message for your group, we will also send that to each member who is not already a member of the new group.
We will send an email to the moderators and owners of the Groups.io group when the transfer is complete.
NOTE: If the new group is a subgroup at Groups.io, you will receive two transfer notices, one for transfering the members to the parent group, and one for transfering the members to the subgroup (all members of a subgroup must be members of the parent group).
Squidge
Has email list servers and archives, but archives appear to be publicly readable instead of password locked to members. Adult content/fan friendly. Dated look, but also hosts pages and files. Probably the closest match to replacing YahooGroups.
https://www.squidge.org/
Dreamwidth
Adult content/fan friendly. It allows explicit material, is free, has threaded conversations, privacy locks and more. Image uploading is limited to 500MB free accounts and 1.5GB paid accounts. Can be set to email comments on your post and replies to your comments, but not primarily an email server.
https://dreamwidth.org
Google Groups
Adult Content not permitted.
May be impossible to transfer. If possible, it's way complicated for those of us who don't write computer code for a living.
https://stackoverflow.com/questions/35966337/transition-from-yahoo-groups-to-google-groups
https://support.google.com/a/thread/17075653?hl=en
https://support.google.com/a/thread/16986960?hl=en
Mobilize.io
Does not appear to have a way to import Yahoo Groups. Unknown position on adult material.
Looks like it has the necessary features, including a free level that handles most of what fan-based groups would need. Includes a mobile app. Geared toward businesses and techies, though. Not a lot of info on what I was trying to find out on their site, and the "ask" link wants name, title, company, email, and phone for someone to contact you back later.
https://www.mobilize.io/pricing
https://www.youtube.com/watch?v=pYoIzl6o8E8
Slack.com
Does not appear to have a way to import Yahoo Groups. Unknown position on adult material.
Not sure which came first, but it looks a lot like Mobilize.io. Free plan only allows access to the most recent 10,000 messages, though.
https://slack.com/pricing/free
https://www.youtube.com/watch?v=6c7_TpPUpL0
Wordpress Plugin
Requires your own hosted Wordpress installation, not WordPress.com.
Moderation, archiving messages, and importing members requires premium version, but unhappy reviewer says it's clunky at best. No mention of whether import includes messages and files, but given the member import apparently is limited to batches of 10, I'd say probably not.
https://wordpress.org/plugins/wp-mailing-group/
GroupSpaces
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
Appears to be all of Yahoogroups functionality plus some, but Free is limited to only 50 members.
http://groupspaces.com/pricing
Zoho
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
The sheer number of apps available is daunting, but Cliq appears to be their closest match to YahooGroups.
https://www.zoho.com/cliq/pricing.html
They also have something called Connect, but the free plan is limited to 25 members.
https://www.zoho.com/connect/pricing.html
Basecamp
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
Doesn't seem to do email at all - instead focused on message boards, chat, online task lists, calendar/scheduling. Does have file storage. The free version is limited to 20 members.
https://basecamp.com/pricing
Wikipedia has a list of some mailing list software, which will require hosting/servers and technical know-how:
https://en.wikipedia.org/wiki/List_of_mailing_list_software
Filehosting and sharing is another whole book's worth of discussion, but if the group itself can't move to a provider that offers all the same pieces that YahooGroups had, it is possible to split the services up to separate providers, if necessary.
morgandawn
Groups.io
Only viable option for transfer, but Adult Content not permitted.
Easy import of YahooGroups, but requires Premium Membership for one year $110 $220. https://groups.io/static/pricing
For some reason, they require login to view the process, so I'm pasting it here:
Due to the pending discontinuation of many parts of Yahoo Groups, we ask that all transfer requests be given the go ahead no later than December 1, 2019. We will not be able to guarantee any transfers submitted after that. Also note that it appears that most Photos sections are currently having an outage and it isn't known if they'll be restored prior to the deadline.
Easy Yahoo Group Transfer
Have a Yahoo Group that you want to transfer to Groups.io? We've made the process easy. Please read all of the following, as some of it has changed.
What We Transfer
We can transfer members, archives (without attachments, however), photos, files, links and databases. Calendar entries are not copied at this time.
Premium Group Required
For the transfer, we ask that you sign up for the Premium Yearly plan (you can downgrade to free after a year if you wish).
Steps To Transfer Your Group
These steps must be done in this order otherwise the group transfer process will not happen.
1 Create your new Groups.io group and upgrade it to premium for a year.
2 Set up and start the transfer process by clicking the Set Up New Transfer button, below. You'll be asked to select your Groups.io group and for the name of your Yahoo Group.
3 Send an invite from your Yahoo Group to transfer@groups.io
4 We will accept the invite and then send you an email directing you to make the transfer@groups.io member a moderator.
5 After you have made the transfer@groups.io member a moderator, return here, select your Existing Transfer transfer, and tell us that you are ready for the transfer to happen. Your group must be signed up for the Premium Yearly plan.
6 Once we receive the go ahead, as soon as we are able, we will download the member list and other parts of your Yahoo Group and directly add your members to your new Groups.io group.
Notes
We do not make any changes to your Yahoo Group. We simply make a copy of everything.
We will add all members that are currently confirmed and not bouncing to your group. Members' subscription preferences (email, no email, digest, etc.) will be preserved. Members' posting privileges (group default, override - moderated, etc.) will also be preserved. However, moderator and co-owner status will not be preserved, so all moderators will need to be reinstated after the transfer. If someone is already a member of your new group, we will not change anything about their subscription.
Unless you specify otherwise, we will send a notice to every member telling them about the transfer.
If you have created a customized welcome message for your group, we will also send that to each member who is not already a member of the new group.
We will send an email to the moderators and owners of the Groups.io group when the transfer is complete.
NOTE: If the new group is a subgroup at Groups.io, you will receive two transfer notices, one for transfering the members to the parent group, and one for transfering the members to the subgroup (all members of a subgroup must be members of the parent group).
Squidge
Has email list servers and archives, but archives appear to be publicly readable instead of password locked to members. Adult content/fan friendly. Dated look, but also hosts pages and files. Probably the closest match to replacing YahooGroups.
https://www.squidge.org/
Dreamwidth
Adult content/fan friendly. It allows explicit material, is free, has threaded conversations, privacy locks and more. Image uploading is limited to 500MB free accounts and 1.5GB paid accounts. Can be set to email comments on your post and replies to your comments, but not primarily an email server.
https://dreamwidth.org
Google Groups
Adult Content not permitted.
May be impossible to transfer. If possible, it's way complicated for those of us who don't write computer code for a living.
https://stackoverflow.com/questions/35966337/transition-from-yahoo-groups-to-google-groups
https://support.google.com/a/thread/17075653?hl=en
https://support.google.com/a/thread/16986960?hl=en
Mobilize.io
Does not appear to have a way to import Yahoo Groups. Unknown position on adult material.
Looks like it has the necessary features, including a free level that handles most of what fan-based groups would need. Includes a mobile app. Geared toward businesses and techies, though. Not a lot of info on what I was trying to find out on their site, and the "ask" link wants name, title, company, email, and phone for someone to contact you back later.
https://www.mobilize.io/pricing
https://www.youtube.com/watch?v=pYoIzl6o8E8
Slack.com
Does not appear to have a way to import Yahoo Groups. Unknown position on adult material.
Not sure which came first, but it looks a lot like Mobilize.io. Free plan only allows access to the most recent 10,000 messages, though.
https://slack.com/pricing/free
https://www.youtube.com/watch?v=6c7_TpPUpL0
Wordpress Plugin
Requires your own hosted Wordpress installation, not WordPress.com.
Moderation, archiving messages, and importing members requires premium version, but unhappy reviewer says it's clunky at best. No mention of whether import includes messages and files, but given the member import apparently is limited to batches of 10, I'd say probably not.
https://wordpress.org/plugins/wp-mailing-group/
GroupSpaces
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
Appears to be all of Yahoogroups functionality plus some, but Free is limited to only 50 members.
http://groupspaces.com/pricing
Zoho
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
The sheer number of apps available is daunting, but Cliq appears to be their closest match to YahooGroups.
https://www.zoho.com/cliq/pricing.html
They also have something called Connect, but the free plan is limited to 25 members.
https://www.zoho.com/connect/pricing.html
Basecamp
Does not appear to have a way to import YahooGroups. Unknown position on adult material.
Doesn't seem to do email at all - instead focused on message boards, chat, online task lists, calendar/scheduling. Does have file storage. The free version is limited to 20 members.
https://basecamp.com/pricing
Wikipedia has a list of some mailing list software, which will require hosting/servers and technical know-how:
https://en.wikipedia.org/wiki/List_of_mailing_list_software
Filehosting and sharing is another whole book's worth of discussion, but if the group itself can't move to a provider that offers all the same pieces that YahooGroups had, it is possible to split the services up to separate providers, if necessary.