Employer giving me ultimatum to keep job [california]

Location: California

I am a waxer at a large waxing chain and I also run my own small business doing aesthetic work which also includes waxing. I do not crossover over business. I have never solicited services at the large wax chain for my small business. My manager found out that I am running my own small business and gave me an ultimatum of keeping the large wax chain job or going completely out of my own. I mentioned that thought that there is a noncompete in California and apparently in our policy, they have something forbidding us of opening up our own business or working anywhere without their permission even though we are non-exempt hourly employees. I also mentioned that I’m not using any of their supplies. I’m not using any of their techniques and I’m not taking any of their clients, but they said it doesn’t matter. They are giving me a week to decide.

Can they fire me for this? I thought I was well within my rights.