Just to be clear, limiting free speech is already allowed to a degree. The Supreme Court has long ruled that it's legal to constrain the right to expression based on time, manner, and place restrictions, so long as those restrictions are content neutral, serve a legitimate public need, and are minimally restrictive to serve that need.
This law absolutely does not qualify. I'm sure they will argue it served some bullshit need to prevent disruption to campus activities, issues with policing, public safety, etc. But there is no chance that restricting all 1st amendment expression on a college campus for nearly 12 hours a day serves any legitimate public need in the least restrictive manner to serve that need. It will certainly be struck down as unconstitutional by a sensible judge somewhere along the way.
But the problem is that this law is not the goal. They want a judge to strike it down. That is the actual goal. That is why they keep passing such blatantly unconstitutional laws in red states pertaining to religion, free speech, lgbt rights, etc. They are doing it for 2 reasons A) They are trying to make the legitimate acts of the judicial branch out to be some sort of overreach on the will of Trump and conservative states to help remove stopgaps that they can't control from their way entirely. That's what the SCOTUS' ruling against national injunctions for lower federal courts was meant to hinder. And B) when it does get ruled against, they just have to keep appealing until they get to the Supreme Court and let the right wing nuts redefine our 1st amendment rights to suit their desires for the entire country, not just Texas. Even if this particular law doesn't survive their decision, again, that was never the point. You can bet your ass that even in striking the specific law down, they will set new precedent with the case that will fundamentally weaken free speech rights for all of us. It will make it easier to implement draconian laws like this on a national scale.