Last week, Saturday Night Live aired a segment where a young performer, Pete Davidson (sorry, I don’t know who he is other than the fact that he apparently had a brief engagement to a pop singer and looks a bit like he could be Jim Jarnusch’s kid) apologized to Dan Crenshaw for a pretty crude joke he made about Crenshaw’s eye patch. (Crenshaw lost an eye in Afghanistan).
On the 11/11 show, Davidson apologized, and then Crenshaw came on and they did a pretty funny segment together (saw it on youtube, not an SNL watcher). Davidson seemed sincere in his apology and Crenshaw was a real gent and a good sport, and it came off looking like bygones were bygones.
IMHO, that’s pretty much how it should be. If you offend, you apologize, the offended party accepts the apology and you both carry on. Unfortunately, this doesn’t seem to be the way both sides regard apologies. There are no drastic or real world consequences when the left gives offense - they expect to be forgiven and generally are. However when they take offense - as in their response to Mel Gibson or Roseanne Barr - apologies are not enough to avoid serious career consequences.