Sure, people have the right (and possibly a moral duty) to speak against those who they believe to be immoral advocates of the wrong belief.
"Feeling alienated" because others don't agree with you is a reasonable result; I mean, this is a zero sum game, all viewpoints can't be most popular everywhere. But it crosses the line when it comes to actual discrimination in the workplace, which is bad no matter whether it's done by or against the nationally dominant "tribe". If people have to shut up or face personal consequences (as opposed to getting ignored because the voice of others is considered more sane), then "You have every right to speak" has failed.
If I can say whatever I want but my political opponents (who want to implement evil policies for immoral reasons) can not, then we don't have free speech. Even if someone rabidly opposes free, inclusive, diverse society, says so, and gets punished for that - that's not a free, inclusive, diverse society; just as in that overused "Voltaire" (Evelyn Beatrice Hall) quote.
Political opponents will always consider and label each others policies and arguments as immoral and unacceptable, as you say, extreme and noxious; so unless we allow (in practice, by ensuring that people don't get punished for that by others) speech that seems immoral, unacceptable, extreme and noxious then we ensure that the political opposition doesn't get free speech. People should be able to talk in our workplace about why they like the noxious candidate and why the evil policy is needed (to achieve the immoral reason) without me or the workplace punishing them - otherwise I might not be able to talk in our workplace about why I like my candidate and why I want to have the opposite policy for incompatible moral reasons, which seem immoral and evil to them.