I don't care if this makes me an idiot or ignorant, but no matter what anyone says, no matter who they are and what degrees they may have, I will continue to believe that the two are compatible in every sense. I'm not going to explain my position, as I don't want to argue over this, especially not on this site given that majority of the people here just want to create a giant circle jerk of arguments while saying "Nuh uh! You're wrong!" it's pretty childish and overall trivial. In short, I believe (and will continue to do so) that the two are compatible and that you can support both without compromising the other (I've had many teachers that were good examples of that).