Uninstall all DLC except for the free Atlas Gorge map.Then you can join their matches using your friends list.There is also a forum topic with almost 2000 replies at Go in reverse chronological order and add everyone that posts there.
If you manage to party up with someone without DLC, this will result in matchmaking working for both of you, since if one player in the session does not have DLC, it will put whole party into matchmaking with people who don't have it either (which is not bugged). Only the built in matchmaking is broken, you can still join games using Steam's "Join Game" functionality. Workaround which allows you to keep DLC installed: