Yes, it's a complex issue at publicly funded schools.
And frankly, in the US, there is an 'Evangelical' aspect which is weirdly different from more mainstream religions i.e. Jews and Catholics probably have more in common than Evangelicals and Catholics - at least culturally. Anglicans and most Protestants go on the Jewish/Catholic side. Even Islam.
A Chapel, a Chaplain, maybe a few religious courses, some influence by the clergy with the school itself, some stricter rules for dorms (i.e. not co-ed etc..) that kind of stuff is one thing ...
... but when everything is 'Gospel Music Only' in the band, 'J for Jesus Cheers', and 'Jesus Revival Rally' before the big game, '4pm Prayer Time', etc. etc.. - it's kind of a another dimension of religiosity entirely. Those kids would be exposed to more integrated religiosity than many of the students at seminary-origin Universities of times past. Oxford Students from hundreds of years ago would think all of that a bit nutty.
I suggest there might be a distinction between: 'Goes to Church on Sunday' and 'Everything is Jesus, Hooray!' kinds of affiliations.
The later, impossible for public schools, the former, possibly.