GMs should absolutely allow third party and homebrew material to their own games. They just shouldn't give anything a free pass because it's in a published book, or written by someone whose name they recognize. That's the point where common sense needs to assert itself. Everything - everything - should be scrutinized by the GM before it's allowed into a game. Whether it's first-party, third-party, or home-brew scrawled on a napkin, you need to look at it before you let it into your game. Even things that are fine in isolation might become broken in conjunction with other material or with house rules, and the only one who knows everything about the game being played is the GM of that game.