The rights of free speech and assembly does not say the govt has to provide you the platform or medium for your activities. For that you're on your own.
A student on his own home computer on his private (not school issued) email or web account could do pretty much anything he/she wants, subject to standard law that everybody has to obey. Likewise, any student may stand at the entrance of his school and hand out leaflets to students. That's all classic stuff.
But when the student uses school-owned facilities for personal expression, it's another story. Students do not have a right of free speech in the school newspaper -- the publisher (the school) has the ultimate say, just as the publisher of any newspaper has the ultimate say in what goes in. Likewise for electronic transmissions -- the hosts of web sites, chat rooms, email networks, etc., have ultimate control.
It is important to remember that publishers and electronic host s are ultimately legally responsible and liable for stuff they 'publish'. This is particularly important when dealing with kids because (1) the original kid who put out something bad may be immune to suit on account of being a minor and (2) the victim of something bad may be a minor and as such have additional rights of law. In other words, if some kids snaps a cellphone photo of another kid naked and then publishes it on the school's media, the school would in a heck of a lot of trouble. This has happened and school officials were in a big mess for failing to protect and control their networks from such actions.
The courts have issued varied rulings on this. Sometimes schools are between in a rock and a hard place -- sometimes they are forced by the courts to let kids publish crap and then they're the ones who get sued over it. Schools have to play all sorts of games to cover themselves.
Accordingly, we see rules like this -- banning some student activity -- so the school can protect itself. Given out litigous world and the fact some kids can be incredibly cruel -- I don't blame the school.
This isn't anything actually new. Even in my day there were a lot of stupid school rules for legal reasons. For instance, we were forbidden to leave school grounds during lunch and the school aggressively enforced it -- even having the cops raid local lunch stops. The thing was, during the school day if a kid got into any kind of trouble (ie hit by a car) the school was liable. Also, teachers/staff were forbidden to transport students in their personal cars (ie give a kid a ride home in a rainstorm) due to liability risk.
When I was in elementary school and learning weights and measures, we had to bring in sample ads from the newspapers as examples. It turned out most of us found liquor ads. The teacher was very upset. It wasn't of course our fault, but the teacher was worried -- realistically -- of having an elemetary school classroom full of liquor ads.