I think it's because there's such a wide spectrum of stories in DW that people become very invested in their particular preferences to the point where they become hostile when things don't match their expectations.

I agree with this completely. The fascinating thing about this show is it's created to be watched on so many levels - a six year-old is going to get something completely different from the text than a male fan or female fan. Where the problem comes in is when people say "my interpretation of the text is the *correct* interpretation of the text". I think there's enough wiggle room built in so that my interpretation of the Doctor as dark and twisted can live along side of the fangirls "teen dream fluffy Doctor". I don't have to agree with their interpretation but it doesn't mean it's not valid.

Like I said below, this fandom is bereft of YMMV. It's all "To the Wall! We will plant our flag and fight to the death!" Who has the time?