Nothing about firing someone would intrinsically prevent them from running for office, unless you fired them for running for office.

What gets you in trouble is not being consistent in applying rules and standards. If you fired one person for a violation but you let other people get away with it, it becomes arbitrary.

No, it means you can't fire them for the fact that they are a candidate.

You can choose to fire them for the fact that (say) they don’t show up repeatedly to their scheduled work. You could even deny them time off they want to use to campaign when they have time off on the books, too, so long as you did so because of legitimate business needs where you would have denied a vacation request even if it was not for the political campaign (if the trier of fact in a lawsuit challenging it finds that you did so because of the campaign, that's a problem.)

I don't know why people equate “you can’t fire people for X” with “you can’t fire a person if X”, but only for certain values of X. Like, you can’t fire a person for their gender, but no one thinks that means you can’t fire a person if they have a gender.

Also, people who work in politics are allowed to run for office, and people who run for office are allowed to work in politics, so what specifically do you see as a conflict of interest? Remember, the company claims this wasn't about politics, so your answer can't involve politics.