I know you said “cinematic universe only” but considering how the EU as early as 1977 interpreted R2 and 3PO’s role in the SW universe as more or less slaves I’d say it’s at least very heavily implied. It’s the kind of detail that’s not really necessary to put into in a movie, but there’s plenty of hints towards it. First off all Luke’s relationship to his droids is definitively treated as an exception. Han clearly doesn’t seem to care for droids, but Luke and Obi-Wan treat them with respect. Even the Rebels in general don’t really seem to care that much about them.
Even in TFA Finn seems quite shocked when Poe insists on going back to Jakku to pick up his droid. Rey seems to sympathize with droids, but she is basically just the new Luke so that makes sense, and it takes Finn some time to warm up to BB-8.
I guess the reason why it seems like pretty much everyone cares for droids is because all of the heroes usually does, and they’re of course the main focus of the films.
Treating droids like people nice seems to be SW’s go-to method to immediately establish that someone is a ‘good-guy’.