How do you approach understanding and respecting beliefs that are vastly different from your own?

Fundamentally disagree. Theology should be separate from politics.

I respect others beliefs which differ from my own as long as it does not infringe on my life.

I believe people have the right to their own beliefs, but I don't believe religious beliefs should affect non-believers

Separation of religion and state, individuals should be free to practice their religion, but it shouldn't affect government policy.

It depends what the beliefs are, If it's about different religions, it wouldn't bother me one way or another. If it's a belief that e.g. women or racial minorities don't deserve the same rights as others. I would think that they have a right to their belief but I have a right to argue and campaign against it.