If you are willing and able to get mods, download SMAPI 3.8.0 from NexusMods and follow the instructions to change the launch options on Steam (I am assuming you are running from Steam, I don't know how to get this to work outside of Steam, sorry). If you launch the game with SMAPI (even if you do not have any other mods at all) then the invite codes will appear and work again. I have to do this myself. If I don't use SMAPI I have the exact same issue.
*edit* I'm sorry, I was incorrect. Running with SMAPI still has the same issue. You need to have Steam running in order to get the invite code options to pop up, regardless of whether you are running through SMAPI or not. (at least as of SMAPI 3.8.0)