A few days ago, I got into a discussion with a friend about religious parallels in New Who - most of all the alleged ones in Last of the Time Lords. I know this is an old meme and has been discussed to death, but tbh, I actually never read any of those discussions, since I wasn't really interested in getting too much into it. Until now ;).
The argument supports a non-religious viewpoint of New Who and contains spoilers up to the series 3 finale (no series 4 spoilers).
Generally, I think it cannot be denied that there are religious references in New Who. Some of the Master's lines are adapted quotes directly from the Bible, after all. So let me clarify what I mean by saying "there are no religious parallels in New Who."
What I'm saying is that I don't think that the Doctor is supposed to be depicted as a god-like figure. I actually think Last of the Time Lords made a point in that respect: elevating the Doctor or the Time Lords to the level of gods is actually wrong.
Of course, there are several arguments that speak against this: the way the Doctor's technology could just as well be magic for all the sense that it makes, the way he's depicted in some episodes like The Satan's Pit, Family of Blood or Last of the Time Lords, the way he saves the world again and again while staying unnoticed by the majority of the population. It's certainly suggested that the Doctor could be like a god to mankind. But I think all these suggestions aim in another direction - they're trying to underline the child-parent relationship between humanity and the Doctor.
The Doctor is a member of a very evolved species who have (or, you know, had) a knowledge of the universe that humans can't even begin to understand. It's a bit like the 'civilized' explorers from western Europe arriving in America in the 15th century and meeting the natives, or like a young child admiring its parents for seemingly being able to do and know anything. However, the Doctor doesn't make use of his superior knowledge to enslave and exploit mankind, like the explorers from Europe did. He certainly could, but he doesn't, sticking to the background like a good parent and doing what he can to ensure that humanity comes to no harm and lives to evolve by themselves.
The Master, on the other hand, does use his superior knowledge to elevate himself to the level of a god. Granted, not a Christian god - not the God of the New Testament. But he definitely sees himself as a vengeful, arbitrary deity who has the right and the ability to decide over the fate of those who fear him. The Doctor stops this; with a method that in the context of Doctor Who science is scientific and un-mythical enough: he channels the power of all of mankind's thoughts through a piece of technology (the Archangel networks) to give himself the ability to defeat the Master.
Now, this brings up the issue of the Archangel networks. Why the name? Well, the Master named that network, didn't he? He picked a name for it that refers to the Bible, but more to the Old Testament, which again underlines his self-portrayal as a vengeful god. The Doctor uses it against him; he sees it for what it is - a mindless piece of technology that can be used by anyone for any purpose - and makes use of it. By doing so, he actually takes the magic out of it; he proves that there's nothing godly or unearthly about a network of satellites.
Using this method - simple, plain old technology - to end the Master's reign of terror is in my opinion a statement about how ratio and science will always have a stronger foundation than religion. It's not meant to elevate the Doctor to a god himself; it's more that the Doctor makes a statement about how making someone a deity simply because they have more knowledge is wrong and dangerous.
Taking all of this into consideration, and the fact that the Master has always been used as a dark mirror of the Doctor's character, I think it's not too far-fetched to say that Last of the Time Lords didn't mean to depict the Doctor as a deity in the sense of a vengeful, wilful god. However, what about the Christian God? Isn't the Doctor and his take on the universe - thou shalt not kill, thou shalt love thy neighbour as thyself - exactly that of the New Testament?
Yes and no. While I do think that the Doctor brings a message of peace and pacifism, I don't think it's a particularly Christian message. You don't have to be a Christian to follow those ethics. Take Buddhism for example - just reading the Wikipedia article gives you a clear understanding that to reach the Buddhist version of salvation, you have to refrain from harming others. Taoism views the Three Treasures 'kindness, simplicity and modesty' as basic virtues, and in Hinduism, your success in fulfilling dharma, the universal principle of law, order and harmony, decides the fate of your karma. "Do no harm" is certainly not a specifically Christian invention.
I think everyone agrees that if the Doctor were supposed to depict a Christian religious figure, it would not be God himself. God as the creator of the universe is too elusive to actually have a walking, talking and acting character mirroring him; and also, if Doctor Who were actually trying to get across a specifically Christian message, it would be a terrible faux-pas to breach the first commandment (You shall not make for yourself an idol.) by personifying God.
Who would the Doctor be, then? One take on the subject would be that he's Jesus; another one that he's the angel Gabriel. Both interpretations prove to be rather flaky on closer observation. Any religious figure in Christianity that is not God lives to serve God. The Doctor doesn't serve anyone, though; he's rather adamant on that matter. The most important thing for him is to be free, to be his own master, and not to be bound by responsibility. He turned down the position of High President of Gallifrey, he despises having to keep to military hierarchy, he's never happy to serve anyone else's will, and never does it for long. The Doctor believes in the science his Gallifreyan upbringing taught him, and that's that.
You could, of course, argue that in this case, time would be the equivalent of God, but that doesn't really make sense, either. Time is indifferent to the fate of the universe; it didn't create it, and it doesn't govern it. Also, time is not eternal - the Doctor knows and believes that there was something before time, and that there will be an end of time.
The Doctor might seem like a god to mankind, because his knowledge is so extensive it seems infinite to humans, but it's all a matter of perspective. From his own viewpoint, the Doctor is as clueless and fallible in his environment as humans are in theirs. This will never change, either, due to the nature of the scientific approach which includes as one of its basic principles that for every answer you find, you also find a new question. Thus, even the Doctor, who seemingly knows everything there is to know, hasn't yet stopped trying to find new questions and answers, because in his beliefs, as soon as you stop doubting what you know, you inhibit any further evolution.
This is, as I think, the message of Doctor Who: a fairly modern, non-religious message of a scientific world view, underlining the belief that to reach 'salvation', i.e. an understanding of the universe, one needs to explore it on a scientific basis and be open to any new concepts, no matter how impossible they seem. They're not impossible, after all. Just a bit unlikely.