Are you talking about flying the flag in the workplace? Then I’d agree you have that right, if in their cubicle they have a Muslim, KKK, black lives matter type of flag, to fire them.
You cannot fire someone due to their flag flying at their home or for taking part in a rally outside of work.
I don’t want to belabor the point as I have to get back to work, but if I, those working for me, or my customers become aware of the flag you fly, the hate you expouse online or in writing, or the protests you participate in, yes, I will fire you. And good riddance. Call it an unwritten morals clause, a compact we have, but at the end of the day I will not hire or employ someone filled with hate, a sex offender, a terrorist, etc. Just like drugs, you can do whatever you want on your own time—legal or not—but actions have consequences, one of which is that an employer may opt to not employ you.