It actually does protect you in non government spaces.

And I don't think you seen the video recently where a manager kicked people out of a restraint for having an anti semetic shirt on and then the restraint got sued when they took it to the courts and it got escalated to the Supreme courts because they said they felt their rights were breached...

Also if a job directly states "I fired him because how the stuff he says outside of work or he wears" they can also be sued. Those type of lawsuits happen constantly and are always a win for the employee.

When you see headlines stating they "fired" the CEO for stuff like that, they never actually fired him, just changed his position in the company as not the CEO... Because it's illegal to fire them unless they said in company uniform which then would violate an employment contract.