However, we have made laws that prohibit certain kinds of discrimination against "protected classes", e.g. based on sex and race.
Being an advocate of gun rights is not a protected class.
Companies are not allowed to do that, but individuals are allowed to discriminate even "protected classes". I can freely choose not to associate with black people, for instance. And that is a good thing. So even today there is a legal distinction between individuals and institutions.
And in a certain sense, "advocate of gun rights" is a protected class, because you have also non-discrimination (I would assume, like most civilized countries) on the basis of political opinion.
Actually, political opinion is not protected against discrimination. Otherwise I could create a political party that advocated, say, the extermination of a particular group, and then if you refused to hire me (because I'm obviously an asshat if I hold this view) I could sue you.
This is decided in court anyway, so the scenario you point out, while plausible, is only theoretical.
In any case, there isn't yet a gun-rights-maximalist party against which YouTube could be prohibited from discriminating.
I was born in a totalitarian country, and so I don't find "you can choose your political views" very convincing.
What about religious views? You can choose these as well.
Freedom of speech and political expression is very different from your right to not be discriminated against for expressing your political views. I will defend your right to say "poor people should not be able to get healthcare", but having this political opinion provides important information on your character, which seems very legitimate to consider when making, e.g., a hiring decision.
There aren't easy answers here, and laws and policy are blunt instruments that will usually have some unintended and undesirable consequences.
I don't know. Can you explain, why should private companies be not allowed to discriminate, but allowed not to have free speech? In both cases you can say, well, if you're discriminated by a private company, you can always go to a different one.
I my view, the problem is that we don't want to force people (individuals) to non-discriminate or allow free speech. But institutions, it's another matter. If the institution has enough power, it can impede the rights of people.
So people asking for YT and such to respect freedom of speech are asking for them to be treated as institutions, something that is potentially more powerful than individuals. And they understand that freedom of speech (just like non-discrimination) is beneficial (for society) in any institution, not just government. After all, you can select a government too, by emigrating into a different country.