I have a F2 visa now. Can I start a non-profit organization in USA?

Thank you!

There is no restriction on race, gender, or nationality, but the question is how long you can go with this since you rely on your spouse's status.

I don't see exactly how what kind of visa you have has anything to do with whether you can form a not-for-profit corporation in the U.S. It depends on the law of whichever state or other U.S. territory it is in which you want to incorporate, but it's very unlikely such law would even require your physical presence in the U.S.