The Catholic Church should note this as they push for "vouchers" to keep their schools from closing. Either self-fund, or fold.
I think the bright distinction with vouchers is that they are given to individuals, not groups. For example, many Americans qualify for the GI Bill. If you qualify for the GI Bill, you may use those funds at (most) any accredited US university, to include many religiously affiliated universities. Also, you may use those funds to earn an undergraduate degree in divinity. So far, the Court has not found an constitutional infirmity with that process.
So, while the Catholic schools may benefit from students redeeming their vouchers at their school, it's unlikely that will undermine the Church's ability to control their religious teachings at those same schools - so far.