I've never read Classic Who fic without looking for specific characters, so I hadn't noticed, but ugh, I can imagine how frustrating that must be. Though I have to admit I've mostly just tagged my DW fic with "Doctor Who" - I figured because both the Classic Who and the New Who tag encompassed a lot of different eras, everyone was looking for pairings or characters anyway ...

(My current fandom has a similar mistagging problem, with novel vs. TV. The TV version is an adaptation, but a very different one with completely different worldbuilding and different characterisation, and people tag everything with the TV tag anyway, whether it applies or not. *sighs*)