I don't arbitrarily bar any publisher.
That being said, I have not been impressed with the Mongoose books I have browsed. Seeing a few comments here, maybe I need to check the reviews on Mongoose stuff the next time I am looking for a supplement. Perhaps they aren't as all disagreeable to me.
If I had a player that wanted to use material from any book, I would review it and be sure it isn't going to become a problem for the campaign at the time. Of course, I can work a lot of stuff in, but I do try to maintain some specific flavors within my campaign. _If_ there was something that I found objectionable, I would further work with the player to find a suitable compromise/alternative.
So, arbitrarily banning a publisher doesn't sit well with me.