So, in how many ways will this fail?
1. First amendment
2. Commerce clause
3. Bill of Attainder
About #3, a Bill of Attainder is a law made to selectively target one person or entity. The Constitution specifically prohibits such things.
As the law is written, any message board or blog would qualify as "social media", meaning that any moderation anywhere would be illegal. Conservative social media spots, which are the most fervent censors out there, would have to stop censoring. Losing the ability to censor would be unacceptable to conservatives, so Florida would have to try to qualify things so that the law only applied to Facebook and Twitter, and that would make it obviously a Bill of Attainder.