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.
