The fact is that bosses can do whatever they want. In the United States, all workers are “at will” employees who serve at the behest of the employer, unless they have a union contract or personal services contract that gives them protection. By-and-large, normal Constitutional protections do not apply to workplaces.
The EEOC nominally protects certain “classes” of workers from discrimination on the basis of: “sex; any group which shares a common race, religion, color, or national origin; people over 40; and people with physical or mental handicaps.”
However, these protections are weak, limited and require massive resources and time to pursue in a complex bureaucratic/legal process. And of course they only apply to citizens.
In any case, any non-contracted worker (and many who work under contracts) can simply be fired for any reason or no reason at all.
What bosses “should” do is irrelevant. What they have the power to do is all that counts because that’s both law and doctrine in the U.S. employment jungle.