LDS release time is every day. The typical case is to have 1 or 2 classrooms in a building adjacent to the campus with full-time teachers teaching during every period. Students can then work the release time class into their schedule easier. (this only happens where there are enough LDS students to justify the church's cost of hiring full-time teachers.) Everywhere else LDS students participate in early-morning seminary (as I did) or home-study. The only time I ever had a conflict was when Traffic Safety was only taught before school, so I missed seminary for a quarter to attend that.

Students using release-time obviously don't get high school credit for the class and must still meet the same credit requirements for graduation. Some of my cousins who live in Utah told me they opted to take early morning seminary (before school, same as I) so they wouldn't miss out on an elective class they wanted. I can understand that, because I had a number of classes I loved in High School and would not have wanted to miss. My senior year I only needed to take 3 classes each semester in order to graduate. Of course I had to take more to fill my day, but when I dropped one because I thought it was pointless the counselor didn't make me replace it with something else. Instead I spent the hour in the library doing my own thing.

As alcarey hinted at, anybody could constitutionally come up with a release time program if they were able to generate an interested student body, get parental approval for every participating student, and have a convenient place to meet off-campus that wouldn't impact the rest of the school day. The LDS programs meet all those requirements. Just because they are the only ones to successfully do this doesn't make it preferential.