I have a few stick-on child safety locks, such as this one found on Amazon.
When it comes time to remove them, what should I do to avoid destroying the finish on the appliances? They are stuck on really well and won't budge by hand.
Try removing it first without removing the foam backing. You can dissolve the foam backing with constant application of WD-40 and scrubbing with a wet wash cloth. We had put some of that foam sticky tape on an old apartment door once and I found that by spraying it with WD-40 and scrubbing it, I was able to remove the foam tape and residue easily without removing any underlying paint or finish.
If the adhesive is 3M VHB (Very High Bond), which I think is what they use for the 'command strips', and it doesn't have a foam backing on it, you can just put firm pressure on it to try to twist it. Hold it there under pressure, and it'll slowly release and pop loose after a few seconds.
If it's foam backed, this won't work, as the foam will absorb the force, keeping it from being applied to the adhesive.
Depending on the condition of the surface, how well the surface was prepped, and how long it's been left on (which I'm guessing is months), it's possible it might damage things -- I've had a number of times when I've taken paint off of walls with the stuff. Hard plastics and shinier finishs seem to hold up, so most appliances should be okay.