I occasionally use the old joke that I don't have insecurity issues, I have a subscription, but poly hasn't really changed my insecurities about relationships much. If anything it's actually helped, because in Tonberry I have a friend whose default response to me expressing interest in someone is "well, don't get your hopes up". Even after I started dating her I had friends who were telling me to be prepared from when we break up because it's going to happen eventually... thankfully not all my friends are so "supportive" anymore.
My poly insecurities, in the end, stem from my personal insecurities. I worry that Tonberry will find someone better than me (more experienced, better able to provide for her, better looking, etc...) and I'll end up becoming a secondary instead of a primary. I'm glad that my only metamour has been quite clear that he doesn't want that to happen, which helps, but during my bouts of depression I do get very anxious about it.
Beyond Tonberry, I have insecurities about dating, because with the exception of her I've never had any luck with it, period. Now I'm going back onto the dating scene with a wife, with raises questions to a lot of people instantly. I worry that I'm just setting myself up to be heartbroken again and again, much like how things ended up with J.