Facebook groups work. The problem is what Facebook does with the data around them: who is in the group, when you post, what you respond to, how long you dwell on certain posts. That behavioral data is the product being sold. You're using a free community tool and paying with your attention profile.
Signal groups are end-to-end encrypted, support up to 1,000 members, have voice and video calls, polls, reactions, and file sharing. For a neighborhood group, family thread, or sports team chat, they're indistinguishable from WhatsApp and strictly better than SMS threads.
The practical challenge: getting people to switch. The approach that works best is to not ask for a wholesale move. Start a Signal group for the people who are up for it, run it in parallel for a month, and let the quality of the experience do the selling. Most people who try it don't go back.
For truly large community groups where Signal isn't practical, Discord is a much better alternative to Facebook Groups. No algorithmic feed, no ad targeting, and the moderation tools are substantially better. It's free and works on everything.