I assume you mean the cabinet is screwed into the wall, not the door?

Is the cabinet wood or pressed board?

Molly anchors are about as solid as you can get into regular drywall.

They normally require at least a 1/4 inch hole, so you may be able to enlarge the existing holes for them.

Opening the wall to install blocking (wood attached to the studs) would be more solid, but would require some drywall patching.

Thank you both for responding. I will try to install the Molly anchors first and then screw the door back on.

Is it best to screw in one one of the two screws through the top hinge in first, then one of the bottom or does the order not matter?

My DH was a cabinetmaker. We never used an anchor of any kind.I think it would interfere with door closing all the way. A little bit of wood in the hole,take a toothpick & break it into about 3 pieces. Try 1 piece in hole if still loose use 2 pieces,(they shouldn't stick out of the hole) don't fill the hole as you need to get the screw in & started. I would do 1 top & 1 bottom screw 1st & be sure you can open & close the door before doing the rest of them. Flat toothpicks are easier to use. Can be bought in any grocery store & maybe even 99cent store.

I've never come across a cabinet door screwed into a wall. What sort of cabinet is this?

Are you in an older mobile home with paneling on the walls?

You might want to make a faceframe and mount the doors to it if possible. If you dont have those skills/tools, hire a pro such as a handyman that has woodworking skills. Make sure they are reputable and ask for references geared towards your project.