That does seem to be a thing.They don't believe in freedom of speech. They believe in freedom from being held to account for anything they do or say - and only for them and their mates.
If someone doesn't like what you've said, and refuses to deal with you again, or do business with you because you're allowing stuff that goes against their principles, that's not them infringing on your "freedom of speech" it's them exercising their rights.
It's also funny when people think that the first amendment means private companies cannot have their own rules, and even funnier when they can't seem to grasp that the first amendment has some limits, and that outside the US other governments may or may not have similar laws but also might have tighter restrictions in some cases because in their recent history they've seen exactly what happens when it's left unchecked. Apparently one of the best ways to filter out the neo nazies pre musk was to set your location to Germany, as the twitter system back then would apply an algorithm that took into account that pro nazi stuff is actively illegal in Germany.
What's possibly funniest is a libertarian type who thinks businesses should be free from as many (all?) regulations as possible can't understand that another business might not want to anything to do with yours if your business is seen as being bad to be associated with.
It's also deeply amusing the idea that large, often conservative companies are "woke"* because they don't want advertising sitting next to stuff that actively goes against their carefully cultivated PR image that in some cases they've spent decades and untold billions creating. For example Coke and their "I'd like to teach the world to sing" advert and literally decades of "it's the drink for everyone to enjoy" stuff really doesn't sit well next to posts calling people inferior and needing to be "dealt with" due to a difference in skin colour or religion.
*Or don't have a very good idea of who buys their stuff and what they think, and have people involved in decision making whose job is specifically to try and make sure that if they make a public statement or do something it's less likely to have an adverse effect on the people that are "profitable" now and understand the trends for the future (IIRC one of the reasons Disney get so much flak from some idiots is because Disney knows exactly how much of the market is untapped/unrepresented and how much money there is in the likes of the "pink" dollar and various markets and aim content at them to get that sweet sweet merchandising money)