Is it possible to find a man ok with abstinence until marriage?

From what I've seen, most adults aren't interested in a relationship that isn't going involve sex.

I've been married before, but have never had sex outside of marriage. I don't want to spend the rest of my life alone (I'm 27), but it seems impossible to date without sex. The situation only gets worse because I'm not a virgin. Somehow, saving yourself for marriage is applauded, but it's just seen as prudish and judgemental post divorce.

How do I navigate the dating scene? Hopeless?