I have a major fruit gnat problem in some of my houseplant's soil. Repotting isn't really an option.

They wont hurt your plants, however they are annoying!
Fresh peppermint & peppermint oil will deter them, however they will just move elsewhere. There are multiple ways to rid your home of them after they move off the plants. Apple cider vinegar and a drop of dish soap in a dish will attract and then kill them. Good luck!

Make a trap for them. Make a funnel shape out of a coffee filter, and punch a tiny hole at the bottom. Attach it with a rubber band to the top of a plastic cup filled with a half inch or so of wine vinegar. The gnats will climb down the filter and into the cup, but won’t be able to climb back out. You chose how you want to dispose of them.

they won’t be “fruit gnats”, but fungus gnats. The larvae feed off of microscopic fungi down in the soil of plants that the soil stays wet. If the plant allows, let the soil dry out before watering it and watch how much you water in the future. Supposedly a half inch layer of sand on top of the soil creates a barrier they won’t get through… from a nursery you can find Bt products that is a bacteria that only effects the larvae…any water based insecticide solution, even diluted down will kill the insects in the soil as you water the plants.
Yes they will damage the roots.