Possums are generally a beneficial animal. They eat rodents and slugs. They are also not very prone to getting rabies, although this is a danger with any wild mammal, I've read that possums have a lot of resistance to it for some reason.
They have very short lifespans compared to most mammals of their size. Even though they're about the size of a cat, and cats can live for 15 years (less if they're outside cats), possums naturally only live 2-4 years.
Since the possum is a fully wild animal and not a feral/partially domestic animal like feral cats, I wouldn't recommend feeding it but if you do, I don't recommend trying to tame it. They are generally not dangerous animals if you leave them alone outside, but if you were to upset it or make it feel cornered somehow, it can have a vicious bite and it has powerful claws too. I wouldn't try to touch it. It could also have babies in its pouch and it would need to be in the wild to properly care for them.
I'm more concerned about the fact that if a possum is being attracted to your food dishes, that more dangerous animals might also be attracted to them. Raccoons, skunks, foxes, and coyotes for example are a very big rabies risk and you could expose yourself to their saliva if you touch the bowls with bare hands.
I had a little bit of a scary incident last year when I picked up a bowl with my bare hands and I realized that a raccoon had slobbered all over it. I washed my hands immediately and I thought I might have to go get shots but I had some things in my favor. One of them was that I didn't have any open sores on my hands right then, also raccoons in my area tend to be clean (although they can be rabid). Most of the rabid animals around here in my local area are coyotes, skunks, and bats. Plus usually if an animal is sick then it will show it in 10 days and that particular raccoon had been around for a couple of weeks and only showed up after dark and looked very healthy. Still, I'd hate for you to put yourself at risk like that. There's pretty much no chance of survival if you get rabies. If you get it, you'll die, and it can happen from something as simple as that.
I'd recommend at least wearing gloves when you handle the food bowls as you can also get ringworm, actual worms, or other problems if you've got wild and feral animals eating out of the bowls and then you touch them. Zoonotic disease is something that everyone that feeds animals has to be careful about.