To my knowledge tefilin and tzitzis are distinct in being the only mitzvos in the Torah that are halachically problematic for women. I do not believe this is at all the case for shofar, sukah, 4 minim, etc.
Rama in the Ashkenzic gloss to Shulchan Aruch rules that it is arrogant for women to wear tzitzis, since they are not only exempt but need not wear a 4 cornered garment to begin with. Rama and Mishna Brura prohibit women from wearing tefilin. The purity required for tefilin is prohibitive for those not required to wear tefilin. Some poskim consider both to be male garments and forbidden on that basis.
As a non-posek I am not qualified to judge what high school girls should be doing. I do know that Rama is posek #1 for Ashkenazic Jewry and that these rulings have been accepted for centuries as authoritative. Therefore, the burden of proof is on those who would permit these practices. Whether any posek for these (or other girls) has met the burden of proof, I do not claim to know.
