Tried everything mentioned in this thread, still to no avail. I made sure my settings were identical to my sister's settings, and it didn't work. My sister suggested that I call Xbox support to see if I had reputation issues or some form of a communication ban... And even Xbox was confused as to why I'm not able to chat in game. Party chat while playing works, playing other games and using game chat works, but in game chat on Friday the 13th doesn't work. I am about to give up, and play on my sister's account, lol.
Best of luck with getting a working solution!