I think this is quite interesting. You're right - people are allowed to be offensive. I happen to think that context is important when it comes to free speech. For example, I believe people should be allowed to express racist views, but I wouldn't want to employ someone who expressed racist views as a teacher, particularly if they expressed those views in the classroom.
In the years since television has existed, television companies have made decisions about what is and isn't offensive. So for a long time they wouldn't broadcast sexually explicit content, or people saying the word "fuck". In 1978, the BBC decided that the Black-and-White Minstrel Show was no longer acceptable, and stopped broadcasting it. Right up until the early 2000s, there were shows in which white comedians used blackface, but I am absolutely certain that that would not be acceptable now.
Similarly, ITV dropped The Benny Hill Show because they realised it was offensive to women.
I think the BBC, as a national, publicly-funded broadcaster, has a responsibility to think about what is and isn't suitable for prime time television. They wouldn't show a white person blacked up (on MasterChef or anything else). They wouldn't give a platform to a Holocaust Denier. Maybe they should now ask whether they should allow a misogynistic man to flagrantly engage in a parody of womanhood on one of its most popular programmes.
I think the context of the Fringe - which generally has an "anything goes" attitude, and where audiences explicitly choose the shows they see - is very different.