I have a 2008 Subaru Forester (auto transmission). Am I doing damage to the transmission by not coming to a complete stop before shifting from reverse to first (e.g. slowly backing out of a parking space and shifting into first gear without braking)? Bad(?) habit from when I had a stick shift…
You’re not doing the transmission any good by doing this. I suspect in time that damage will be done sooner or later. I would recommend breaking this habit because transmission repairs are very costly nowadays.
Yes, but that does not really answer your question. The question are you doing material damage. That one I can’t answer for you.
However for the sake of your whole car, especially the transmission and possible passengers, I would unlearn that habit.
That was even worse for a manual. Actually, thanks to the torque converter, you do little damage - it’s like sitting at a light in drive, the engine turns, the car does not. Don’t do it at high speed, but “almost” stopped is nothing. Though it does put a strain on the engine - if you can bother to ask, bother to stop 
Why gamble? Automatic transmission repair is very expensive. Come to a complete stop before shifting from reverse to drive. It only takes an extra second.
Yes, bad habit. What seems like only a little motion to you is actually a lot of force. Brakes are designed to handle this force, not so for the transmission.
You’ve heard the opinions and I agree. It’s now up to you. The owner’s manuals often say"come to a complete stop".
My little sister does this, drives me mad, because every time she shifts from reverse to drive her transmission goes “clunk” like the noise a manual makes when you don’t quite push the clutch pedal all the way in before shifting. I would say you’re definitely doing more harm than good, that sound is sickening.