It is ironic that right wingers are suddenly enamored with enforcing first amendment rights against private companies. If there are first amendment rights to things like internet website hosting and being able to post on social media, then the following will also trigger first amendment rights inside private businesses:
The right to use an employer's email system to circulate union organizing material.
The right to wear clothing with socialist slogans while making coffee at Starbucks.
The right to stand inside a clothing store selling fur coats while holding up graphic signs showing animals being skinned.
And so on.
And if the consumer is given free speech rights over and above the private business's rights to operate their business how they see fit, the people who refuse to bake cakes for gay weddings would have to bake cakes for gay weddings because they cannot refuse to bake a cake that says "congratulations Steve and Mike on your wedding".
It is fun to play the victim in internet free speech debates with the narrative of a leftist social media world trying to destroy right wing movements (which ironically the social media world substantially participated in creating and profiting off of), but you cannot pick and chose your principles of limited government and the rights of private enterprise when it suits you.