There is a large amount of legal precedent in the US for the government being able to compel speech of private businesses, both in laws and court rulings. If you don't believe me, go look at your nearest "nutrition facts" label. But we have precedents that go much deeper than that, up to and including compelled speech that goes against the religious principles of a business's founders. There is no realistic argument for the government being unable to compel a private company like Twitter to cease censoring posts on political grounds.
Many people and organizations have their free speech regulated because of the ability of speech to do harm (e.g. yelling "fire" in a crowded theater).
Saying something trite about rights is not an argument. these companies have a huge responsibility to our democracy, and treating them as if they're just another company is exactly what allows them to be so cynical about making decisions calculated to increase ad revenue even when they're harmful to democracy.
if the population of a democracy doesnt want to be a democracy anymore, that seems perfectly legitimate
When a platform with this type of power starts abusing it immediately before a major election, it's time to rethink the governmental protections afforded to them in order to feasibly exist.
Twitter isn't the government, and they don't control speech anywhere but on the platform that they own. They could ban the American Flag and they still wouldn't owe anyone an explanation short of their stakeholders who are going to want to know how this factors into Twitter's only business: Selling ads.