This is an interesting thread. There are definitely groups who are obviously Hindu but don't count themselves as being such. For my self i find the following scenario:
1) Person: "What religion are you?"
Me: "Vaishnav"
Person: <<insert funny look>> "huh?"
2) Person: "What religion are you?"
Me : "Hare Krishna"
Person: <<insert disdainful look>> "You belong to a cult!"
3) Person: "What religion are you?"
Me : " Hindu"
Person: <<insert surprised look>> "You can be white and Hindu?"
I prefer scenario 3, the surprise look is nicer than the other two
. I am a congregational member at my local Iskcon temple and I find that my theological views are heavily influenced by them but I don't consider myself as being separate or outside Hinduism or the rest of the temple. They keep Vedic standards and that's enough for me regardless of how Iskcon may present itself.
I can see why Vaishnavism as a whole has tried to make a distinction between itself and other forms of Hinduism but I don't see why Vaishnavs or any other group who accept the Vedas can't consider themselves Hindu or better yet, Dharmis
Aum Hari Aum!