If the voucher goes to the parent, and the parent has choice among religious and sectarian schools, then there is no Constitutional issue. Period. End of story.
What's fun is even if you use vouchers or homeschool and do not enroll your child in the Public Edu system, you still pay the taxes for public education in your area.
Fair? Right?
It's all about $$$.
The schools lose students then they lose funding and money. Dries up their little teacher kitty.