This question seems to assume that Tatooine allowed slavery because it wasn't part of the Galactic Republic. I'm not sure about that. Wookieepedia doesn't address the issue, merely reinforcing the ideas that (1) slavery existed there, and (2) Tatooine eventually joined the Empire.
Let's clear this up:
Did Tatooine ever belong to the (pre-Imperial) republic, and if so, when did it join?
Note 1: Canon answers are STRONGLY preferred over Legends
Note 2: Bonus points if you can provide a link to a list of worlds known to have been part of the republic