The dictionary definition is:
obstinate **or** unreasonable attachment to a belief, opinion, or faction, in particular prejudice against a person or people on the basis of their membership of a particular group.
Hating bigots with a very firm stance would be "obstinate attachment to an opinion, in particular prejudice against a person on the basis of membership of a particular group".. that group being bigots...
So yes, strictly speaking bigotry towards bigots is bigotry, its just proof that not all bigotry is bad.