R Soloveitchik was for dialogue and cooperation on practical matters, but not on theology. Even when catholics decided to overturn their anti Jewish positions in 1960s, he suggested not to cooperate: it is their own problem and they are dealing with it.
On the other hand, straight teaching our position may be different, despite the gemoras ^. we are well past septuaginta, protestants allowed everyone to learn Bible 500 years, and nowadays anyone can read artscroll gemora with meforshim.
I am not saying that this easily justifies any particular interaction, but it at least opens a discussion