Well, I'd say it's more like if you REALLY love Tolkien you'll read ALL of his works and not just LotR. I think that would be an accurate comparison, since people love The Lord of the Rings because of how accessible it is, whereas his other writing, while good, isn't always as easy to get into. In the same way, NuWho is very accessible and easy for people of this generation to understand and like. Not to mention Classic Who requires a big, huge, massive investment of time.
To the OP: I respect the fact that there are a lot of diehard Whovians out there who love the show and have watched every episode at least three times--I do not, however, appreciate it when they tell me I'm not a real fan if I haven't watched every godforsaken old-as-dirt episode as well. So sue me, but I just don't have enough time or interest for that right now. I will get around to the first two Doctors, which are on my hard drive, when I feel like it. And until then, I will continue to call myself a Whovian because like it or not, I am a fan of Doctor Who.
Tons of people love Sherlock but haven't read the original Conan Doyle stories. They are still legitimate fans of the series in spite of that. I've read several of the stories, but I don't think it makes me superior to people who haven't. Fans are fans. Get over it (or, in fact, get over yourself).
Doctor Who has got to be one of my favourite TV shows. I only got into in with the modern series, but right when it came on in 2005. Since then I have gone back and watched some of the classic who episodes, and really want to watch more! I can name all the classic doctors easily and just love the story lines, even if the effects are rubbish. But if people claim to be really into Doctor Who, then they should have at least seen some of the classic series :)
What annoys me is that you can't watch the whole series from the start because the BBC wiped some of the old tapes. I've seen the firstfew eps in black and white and they are awesome, even though they are a little bit terrible. I want to do an old school doctor marathon! Have you got any of the old eps Molly?
I can't watch the modern version. it's just horrible.