I'm having this sort of problem with my current ex-partner. One of his 'conditions' to me being polyamorous is that he should vet all of my partners and the idea behind it is something that rankled me slightly. I tend to go for people who are complete opposites, so there is a definite chance that he will never approve.
The other issue is that sometimes there is just not enough time for him to meet them. We are both very busy people at times and I don't want to keep any potential partners waiting for something that could be a long time coming.
On the other hand however, at some point I would want them to meet but it's not something I'm happy having to wait on his schedule.