Well, yeah, that kinda is what it means.But that's not what generalizing means. When we generalize, we take a one characteristic thing and represent as a whole. If I don't like seafood, it doesn't mean that I don't like all the food that comes from the sea.
I can't imagine that the general term atheist would be used against one particular religion. If I were opposed to Christianty, I'd say so explicity. As an atheist, I'm opposed to gods.So if you are anti a particular type of theist, ie Catholics, Mormans, Muslims etc, you are opposed those particular type of theist. And we generalize it by using the general term, which is theist. That's why it is possible to have an anti-theist Christian, someone being a Christian that is opposed to a particular type of theist(s).