You can use a third party Facebook app like Material or Tinfoil Hat that has messaging built in by simulating an old web browser. It's a little clunky but it at

You can use a third party Facebook app like Material or Tinfoil Hat that has messaging built in by simulating an old web browser. It's a little clunky but it at least isn't always running and has no access to your address book or contacts. The downside that you get no alerts someone responded but I like it. I check on my own time.