So, I was surprised when I first found out about Lily-bashing.
I mean, she only appeared in 10 or so pages, and people were already screaming Mary Sue. I think JKR did describe her as "like Ginny, pretty and popular" somewhere, but Lily didn't strike me as the unpleasant type of "popular girl", if you know what I mean. To me, Lily seems like a compassionate type of person. Even though she didn't approve of Snape's involvement in the Dark Arts, she still stayed friends with him for some time, rather than ditching him right off the bat. Of course, when Snape called her a Mudblood, that was the final straw for her, and she was justified in breaking off her relationship with him, because she knows she deserves better than to be around someone who hangs around people who are racist against Muggleborns and follows their example.
Now, for the record, I actually like the one-sided Snape/Lily pairing better than James/Lily, not because it's healthier (of course it isn't!) but because I find the dynamics more interesting, and it shows a different side to Snape than what Harry sees, while James/Lily is too perfect for me. Realistically speaking though, James was the better choice for Lily, and it's disturbing to see people bash James in favor of Snape. James did change his ways, while Snape didn't. I was surprised when some people called her Lily Sue because she was smart, pretty, and popular and "bitchy" towards Snape. Really? I never thought of Lily as bitchy. It's actually remarkable that she stayed by Snape's side for so long. Imagine the US (which is where I'm from) 60 or more years ago; imagine two friends, one white and one black. The white friend associates with people who are racist against blacks, and this friend then makes a racist comment to their black friend. Surely you won't be bitchy to end that friendship, right?
And I don't think JKR put enough emphasis on how pretty and smart Lily was to make her into a Sue. Lily did not even appear that much. Look at Cedric; he was very attractive, excellent at Quidditch, and attracted lots of girls, yet we don't hear him being called a Stu that much. So while I don't think that the Lily-hate is only due to sexism, it is part of it.