This is where we are right now. The political right in the United States is determined to silence LGBTQ youth at school, and at least in this case, they'll take the nuclear option.
The school board would face a lot of legal risk trying to censor the student newspaper. If they tried to stop the paper from printing LGBTQ content, they would undoubtedly be sued, and defending the suit would be very expensive regardless of the final outcome.
The board would have to mind their p's and q's very carefully, and judges would still probably rule against them very often.
Since the board cannot reliably or predictably control what the students write, they shut the paper down.
And that's where we are in the "Land of the Free," where freedom is meant for conservative religious people, not for nasty queer folks.