The national labor relations act only specifies the conditions under which workers can organize and collectively bargain for certification as a union. It also specifies some modes of arbitration for disputes.
In my view, a business shouldn't be allowed to dissociate themselves from workers for ideological reasons unless it's stipulated in the contract because the business has some public interest. By that I mean they perform a public service people engage with that could be compromised by a worker's expressions of bias. In this case, I'm thinking of government workers and subcontractors. Businesses that are just in it for the profit should have a right to censure workers and maybe even publicly, but to me the idea that you can lose your source of income due to what you believe just for PR face saving is too easily misused and overwhelmingly favors management prerogative. I've been in the position to have people fired for racist remarks they've made to my face in the past and objected because I believe in this very strongly. In a unionized workplace, workers would stipulate the circumstances they could accept for removal and management could object and they could go back and forth until they reached a compromise, including arbitration procedures and what payout they would have to give a person in the event of needing to sever the relationship. Sadly, in modern US society, only around 6% of private sector workers are unionized at all and the majority work in at will jobs where you can be fired at almost anytime just because the boss doesn't like the cut of your jib.