in PA, Catholic students had CCD classes on Saturdays. A woman in our neighborhood offered a non-denominational Bible School class in her home for grade school kids. It was on Thursday afternoons AFTER school.
My family was Lutheran. As kids, we got our Bible instruction on Sunday mornings, in Sunday School, prior to the regular service. When I was in junior high, confirmation classes were held 3 days a week, for an hour and a half, AFTER school. We switched to another Lutheran church shortly after I started the confirmation classes. At the new church, the confirmation classes were held on Saturday mornings for 3 hours, from 9 am to noon.
No need to make a big showy deal out of those classes by scheduling them in the middle of a school day.
One day a year, on Reformation Day, the city's Lutheran Churches held an all day retreat for high school kids at one centrally located church. Kids could be excused from school for the day with a note from their parents, but we were expected to take responsibility for catching up on what we missed in school that day.
In PA, the state law used to require that ALL public school teachers had to begin the school day by reading one full chapter from the King James Bible. It had to be King James, which angered Catholic kids and their parents.
I was 13 when the Supreme Court ruled that it was unconstitutional to require reading religious material, teach religion, or require prayers in public schools. You could teach ABOUT religion, i.e. the effect of the Reformation on European history and politics, but you could not instruct students, such as indoctrinate them, on any religion.
The Sunday after the SC ruling, the pastor of our church gave a sermon in support of the ruling. He said that it was the responsibility of parents, not public schools, to provide religious instruction to their children. It was the only way to preserve religious freedom and that it worked two ways, to keep religion out of government and to keep government out of religion.