Can an employer fire me for having another job?

I am a personal trainer in WA who recently got a second job at another gym. When gym A found out I was working at gym B, they told me that I have to choose and am not allowed to work both. I am not a full time employee of gym A and gym B gives me a stable salary (but still not as much as gym A).
If I quit gym B can I collect unemployment?


Hmmmm. Does Gym A have something in their rules about working for competitors?

If you quit Gym B you probably wouldn't get benefits because the quit wasn't attributable to them.