You could always go the saltwater route. Yes, saltwater pools still have chlorine (the salt cell makes it), but it’s at a much lower level—usually around 1-3 ppm. Your swimsuit will last longer, and your skin will feel like silk.
Or try a UV or ozone system. They zap bacteria with light or electricity, so you can keep chlorine at a bare minimum—like 0.5 ppm. It’s the pool equivalent of using a Roomba instead of a bulldozer.
Honestly, these systems are the future. Your pool stays crystal clear, and you stop smelling like a laundromat.