But R2 and Chopper are still property. They have no legal standing in the society they exist in; if anything ever happened to their masters, they could be sold, confiscated or destroyed as the situation merits. And it's not like their owners really treat them as equals. It goes back to the "ship of intelligent dogs" I mentioned at the beginning. To some people, their dogs are their friends, their family. They worry about them, and try to provide for them a great life. But to other people, dogs are just a dumb animal that can be discarded the moment they become bothersome.
If Luke and R2 were captured by the Empire, they wouldn't even consider negotiating for R2's release; he would be captured property from a dangerous terrorist. He would be dismantled and searched for information about the Rebels. Then sold for parts, or wiped and put to work for the Empire.
Ig-88 must have some standing with the Bounty Hunter's guild; he couldn't be hired by the Empire without the Guild membership (at least not officially). The only other sapient droid that comes to mind is Guri from Shadows of the Empire; and that's because of her status as a Prototype Human Replica Droid, acting as a crime boss's henchperson.