In the second case (that’s easier, so I can answer it first), the relationship would end, sooner or later. I can get along fine with someone who can agree to disagree with me, respectfully, but in a situation like you describe, there’d be no way it could work for me. In fact, there would be a definite limit to how far it would even go in the first place.
In the first case, it would take a lot of discussion and planning to see what we could work with. It would vary more with my potential lover’s personality more than mine–how flexible he/she could be about it, if flexibility was possible on his or her part. As for myself, I would be committed to doing what I could to make it work, up until it would be a huge hassle and more trouble than it was worth for both of us.