The first amendment only applies to state actors. I’m not sure why it’s so frequently used broadly as a blanket for free speech in any context.
If they care about this they can simply ban phones in their school districts.
This suit is analogous to banning fedex and ups because kids are addicted to mailing each other scandalous notes. Clearly will fail.
If there’s specific content posted by specific groups that are a concern the school should go after them.
If that is the reason though, I'd doubt that speech that deliberately attempts to subvert rational thought and manipulate the audience would fall under that protection.