Would definitely be a deal breaker for me. But, that said, I do think that definitions of Left and Right in politics are breaking down somewhat. I'm pretty far left, but I disagree with many of the positions of the left these days.
From everything you've said, I would be very wary. I've come across many men like this before and I think there's a danger in the dynamic that develops whereby they try and convert you, find it a turn on to be with someone different to them, who is willing to espouse views they don't come into contact with that often, then wear you down until either they feel they have "won" or you are just arguing all the time, which becomes tedious and hurtful. Here is a cautionary tale: I have a friend who I went to university with. She was a strong feminist lawyer; left-wing, feisty, charismatic, confident. She had a whirlwind romance with a Tory, ex-public-schoolboy. Their whole relationship was founded on disagreements about politics, but I think she was also drawn in by his money and alpha-male persona. Within a few years, she had given up work and was a SAHP, feeling utterly trapped in a situation she felt was out of her control. The dynamic of debate has degenerated into arguing over everything, and she has moved a long way to the right in her political views. Now that he has worn her down over so much, he has no respect for her, as she is no longer the "feisty, independent lawyer" he married. (BTW, I am a SAHP myself, and totally dependant on my DH's income, but that is even more reason to choose a man who values equality and caring work - if he didn't have a totally egalitarian view of what we both do and it's value, then this wouldn't work at all.)
For me, the most important characteristic in a partner is empathy. The biggest turnoff: materialism, greed and selfishness.