From what I have interpreted from the ACLU's interpretation of the bill, they sound like they are worried this bill will force students to join religious clubs. I don't know of any schools that would force/require a student to be part of any club whether it be games club, anime club, that pusillanimous individual brony club, art club, book club, or paintball club, or whatever other clubs exist.
They seem worried that these students will be forced to hear religious messages and be offended by it. Well propaganda is propaganda no matter what is whether it be ads for buying stuff, to join a charity, religious, nonreligious, nationalistic. At my bus station there is this guy who preaches religious messages all the time, and all I do is ignore him. Simple as that. But they are like "Oh no, I am forced to listen to some Christ cigarette, muh right to euphoria!". I can only imagine the huge backlash that were to interrupt if a group of students were Islamic, Sikh, or Buddhist were denied having a club for the same reasons the ACLU gives.