I hate drama. Jealousy sucks. My wife doesn't climb, but we still deal with jealousy from other situations. I think the only solution involves being extremely mature and having honest (but respectful) communication often.
Usually jealousy is just a symptom of something else, imo. If you are both really honest and open about your emotions while managing not to act like a teenager, then usually reason prevails.
I don't see anything wrong with climbing with an SO -- it just depends on the dynamics of the relationship, I guess.