The argument "if you don't engage in politics then you might be part of the problem", is itself a political argument, therefore it is irrelevant in the context of a no-politics rule.
"recently changed its company handbook to declare it won't ban potential customers on "moral/value grounds," and that employees should not discuss politics at work."
I'm assuming that "should not" means it's discouraged as a culture and not enforced somehow, because otherwise I would think something different. If so the article seems to try and persuade you against this because politics is somehow important, but the whole point of the new rule is to precisely ignore that.
It comes down to whether it's enforced (regardless of how). If there are repercussions of any kind, then in order to make that judgement you need an objective perspective of what's political which is even more of a waste of time if not impossible. Whoever is tasked with discerning what should be punished and what isn't is bound to have some bias.
