Sorry no. Constitutional rights are protections against the government not protections from the restrictions that might be imposed by private business owners. All public utilities are used by private parties. Those parties don’t give up their right to restrict the use of that property by using utilities.
Companies that may feel squeezed by the EU are going to have to choose how to operate. If they choose poorly, their users are free to use other platforms or to create one themselves.
BTW - remembering friends who worked on DARPA. Feeling old.....
But these aren’t just private entities. They use public airwaves. They used public research, etc. The courts in the past have ruled that a mall (ie private property) could not exclude people who wanted to hold political protests on their property because they were effectively the town square.
It was the same in company towns - they too could not exclude people from protesting, signing petitions, etc on their property even though they were private companies because they owned the whole town and thus could not exclude people from the town square.
In the modern era, social media is the digital town square.