Loyalty mission after main story line

You can, but take my advice ... do the Ryder Family Secrets BEFORE you finish the story. I have verified that if you finish the main story before doing Ryder Family Secrets you will not be able to do that mission at all.

As far as loyalty missions, yes, you can do them all from start to finish after the main story. I romanced Peebee early on, then did the main story. After completing the main story I started and did the loyalty missions for the rest of my crew from start to finish.

As far as i can tell all other side missions seem to be attainable as well. The only exception being Ryder Family Secrets. Even though I was almost done with the mission, I got locked out after I finished the story.  I just made a 45 minute YT video proving that one, unfortunately.    It sucks because I consider that mission to be the most integral side mission in the game.