We probably only disagree about whether or not it’s a matter of ideological purity as opposed to creating a hostile work environment (notwithstanding arguments that would define “hostile work environment” in terms of one’s puritan ideals).

I don't know that there's a way to distinguish "ideological purity" from just any beliefs or conventions around what types of speech are appropriate for work.

You absolutely can; just don't define "hostile work environment" in such a way that a person's private (out of the workplace) beliefs would constitute a violation. Sexual harassment and racial slurs in the workplace? Violation. Promoting fascism or communism on your personal Twitter (provided your personal Twitter really is personal and not professional)? No violation. Sexual or racial discrimination in the workplace? Violation. Seems tractable enough to me.

No, a "hostile work environment" is one in which one's colleagues are unable to do their jobs effectively. That should be lawyered more precisely, but we needn't flesh it out here. No one's job depends on everyone adhering to the very narrow ideologies that mobs are enforcing today.