Actually yours is the predominant view of those on the left and HN in general - “they are private companies so deal with it”. From a purely legal perspective, that view is almost certainly correct.
The issue is a societal one. Half the country isn’t just going to sit down and shut up because a few liberal billionaires told them to. They’ll create alternatives, and then we will have not just a philosophically divided country, but effectively two Internets - one for conservatives and one for liberals. Where does it end from there? Do hotels and restaurants in California demand to see proof that you are a registered Democrat before you are allowed to patronize them? Do liberal employers start carrying out mass firings of conservative employees?
We are seeing the beginnings of a country of ~300 million people being cracked in two, on a much deeper level than has ever happened before. I can’t think of something less American than a bunch of business owners ganging together to strangle the life out of a small business because they disagree with the politics of some its users.