Actually I go to a lot of social action groups, political action groups, meetings, UuFN fellowships, etc. And 99% of the time I only meet people that are in my tribe, I.e., liberals. I will look into precinct meetings, that should be very challenging in the trump county I live in. Contrary to your statement, I have built some good friends on Facebook some of which have become friends in my real world...but do your point, they are almost all liberals. I am actually looking for mixed groups, in a perfect world, 1/3 each of independents, democrats, and Republicans, hopefully different sexes and races. However, such groups seem more like a unicorn more than reality.
Moderate-to-heavily involved with junior Rotary in HS. Most of the Rotary members I interfaced with were stand up people active in the local community and further out of different backgrounds. Lots o' people on boards of schools, hospitals, etc. working in their own way to advocate for those who need it (at risk students is one example, hell the org's mission is to eradicate Polio). Volunteer options were sick, too, like staffing the minor booths at the Arnold Palmer Invitational. Anywho. Can confirm, it's a nice option.