Coming from the perspective of 25 years of diving, and technical and full cave diving certifications, I approach it along a continuum.
For the local quarry, I'll dive with just about anyone who does not have an "attitude" or personality disorder. Skill level is not real important and I am more than happy to mentor a new diver.
For offshore trips, I get a little pickier as I invest a lot in the trips and I do want the dive to be enjoyable and not have to babysit a diver or focus on keeping them from doing something stupid and killing themselves.
For cave diving, I may dive with you if you appear to have your stuff togther but I will watch you like a hawk and double check everything you do before during and after the dive (but I try to be subtle and discreet about it.) Until I develop a level of trust in your abilities and your judgment. If I never dive with you again, you'll know why. If you really screw up, I'll tell you exactly why on the spot in no uncertain terms.
Basically, in all three of the above situations, I make the mental assumption that I have the same level of buddy support that I would have on a solo dive and I accept that if things go south, I will be bringing 100% of the resources to the table. I don't mean that to sound negative, it just means I don't assume there will be any assistance avialable to me if a problem develops and conduct the dive accordingly.
There are a few who have made the short list who I love to dive with in a cave, and would indeed trust with my life, but they are very few in number.
On the plus side, I met Marci as a "blind buddy" and she is a phenomenal buddy - one of those really rare people who function on the same wave lenght you do. It usually feels like we share the same brain.