I suppose the equivalent relationship for me would be with a straight man who loudly and proudly insists that he is straight. It would be a serious slap in the face for me.
But then there's my last relationship. My ex had absolutely no interest in men and was so dogmatic about it that we couldn't get past it. If we HAD been able to work out our differences (I wanted a husband, he wanted a wife

), then things would have been very weird indeed. He identified as straight, period. Because of our twenty-year relationship, he was willing to at least try to make things work, for a little while. Obviously, that didn't last.
I don't know what our staying together would have done to his self-labeling. Actually, he didn't tend to bother labeling himself as straight, probably because straight is a default orientation that usually requires no overt labeling, for most people. So I dunno.
Then again, he is just queer enough that it might have worked for me. I call him a part-time lesbian because he always played lesbian characters in his computer games. With other lesbians, no less. I'm quite sure he isn't trans, but he is...trans-ish in this one way. It's just fantasy.
But if I were to start a new relationship with a straight guy, I don't think I could ever get past the "straight" label unless he changed it. I've worked too hard and gone through too much to be in a relationship where the other guy stubbornly labels himself as straight. And if you think me too dogmatic and inflexible in this respect, then what does that say about the other guy?