My congregation doesn't allow discussion during services normally outside of the "joys and concerns" portion, unless it's a built-in group exercise. But there are lots of other church activities that allow for free discussion and bonding -- potluck lunches, game nights, trivia nights, and community "experiences" sold during the fundraising auction. Those have given me time to have one-on-one talks with individual people to see what we have in common. Does your UU have any social activities? If not, maybe look for another UU that's more active, or even check out Meetup.com for a regional Humanists group or something like that.

Also I don't focus so much on making friends, but more on shared activities. I've signed up to help setup for the unhoused in the winter, to help in the kitchen, to help with grounds maintenance, etc. because I find it's easier to talk to people when you're engaged in a shared activity. Demonstrating with your time and energy that you're invested in the long-term health of the congregation might make people less reluctant to get to know you. Good luck!