I don’t think “keeping quiet” is always a cop out. Sometimes where the differing points of view can’t be discussed and a compromise reached (as here, you can’t half leave or partly stay in the EU) so if you are discussing it quite fervently, as sounds the case, you are both trying to get the other person to see your own, strongly held, point of view. It isn’t going to happen. Not discussing it further seems sensible, as there isn’t really any point in doing so.
It wouldn’t bother me we had a different view, but ridiculing your view is another thing altogether. You don’t say if he respects your views in non political discussions, but if he does, that for me, would be a sign that we had no future together.