I think the issue is “How do you decide what is political and what isn't?” e.g. if you're a communist, then the existence is shareholders is political support for capitalism. So how do you remain “apolitical” then?
Outside of your job, you can be as politically active as you wish. Nobody is saying you should stop all political activism.
But if i walk into a store intending to buy something, i don't want to be blasted with any political message or be asked to sign up for a rally or donate to some cause i don't care about.
And an employee should work on the job they are being hired to do, not spend work time undertaking political activism unless explicitly allowed by their boss (for example, your company may allow you time off for charity or such activities).
If, for example, your political view is that of communism, then you will have to suffer in silence in the USA while working for shareholders/owners of property. Or quit your job if you cannot stand it. What you can't do is use your job as a resource to push that view further than you could on your own.
So you take this political stance outside of work. If enough people can be convinced that collective bargaining is a good idea, it will get enshrined into law. Employers will have to comply.
On the other hand, organising during work time (which is being paid for by your employer) is unethical - and regardless of my feelings of the idea of collective bargaining, it should not be done on someone else's dime.
I dunno where you live, but organizing at work is a protected right that workers have in the US and Canada (and other jurisdictions, but that's where I've been employed). An employer forbidding that is actually a violation of labor law.
You are only political when you try to change the minds of others. Just existing is never political support for anything. If the communist argues that the shareholders shouldn't exist then he is political. If the company fires the communist for thinking that shareholders shouldn't exist (lets say he said that on his own time, so he wasn't political at company time) then they are political. If the company allows pro capitalist opinions but not pro communist opinions they are also political.