Conservative Americans are traditionally all-in on respect for private property. One doesn't expect to go just walk on someone's lawn and put up a sign without the owner's permission. I honestly don't understand why the same respect doesn't apply to the services provided by private companies like Twitter and Facebook.

These companies spend billions of dollars annually on infrastructure and engineering to host user content. How can Republicans be asking the government to step in and dictate over that multi-billion investment? Doesn't that fly in the face of everything they believe about government's role in the private sector?

In your example, of course the pro-life CEO can do whatever they want with content on their site, assuming it was uploaded by users within the site's terms of service. If someone were actually paying for hosting of the content, they would have a case to get upset about having it taken down. But that's not the kind of contract that users of social media sites have made with the companies.