Oh my gosh come to All Souls UU church in Columbia Heights!! It’s exactly what you’re looking for. There are tons of families, we do a monthly parenting potluck after services that’s a great way to meet folks, and an annual Weekend on the Bay that’s also great. The kids start in the service, and then go down to RE (religious education) which is really fun.
All Souls has been a leader in social justice and activism basically since its founding - the DC marriage equality bill was actually signed there. They work closely with Free DC and other orgs, there’s a whole group on voting rights, really anything you can think of!!