The costs outweigh the benefits to you, probably because the status quo is pretty favorable to you. This may not hold for other people, except now they're gagged from doing anything about it.

They're not gagged, they can still engage in political activity, just not on company time.

And not against others at the same company.

No, that doesn't follow from "not at work". You can engage in political activism outside work, even if somebody from the same company is active on the other side. Both of you are asked to not turn work into the battle ground however.