>but I figured a lot of private companies already do that,
Not all of them. Lots of organizations, mainly religious, are more than willing to discriminate against LGBT people. There are big controversies over gay teachers being fired from their jobs in Catholic schools after coming out. This is why we need federal laws covering this issue, and NO RELIGIOUS EXEMPTIONS!
Those are religious private schools. I agree it's still a shitty thing to do but religions have loads of protections. What is there to be done.
If they get fired from public school, then yeah absolutely.