...I am not aware of this type of outreach that takes the place of academic programs (usually it's things before or after school).
The
Zorach v Clauson case (follow the link to check for yourself) that they cite as their constitutional justification was explicitly about releasing students during mandatory school hours. I'm quite familiar with all of the religious liberty cases as part of my study of church and state issues in seminary, as well as my own personal study over the last 30 years:
The opening sentences of the syllabus:
Under § 3210 of the New York Education Law and the regulations thereunder, New York City permits its public schools to release students during school hours, on written requests of their parents, so that they may leave the school buildings and grounds and go to religious centers for religious instruction or devotional exercises. The same section makes school attendance compulsory; students not released stay in the classrooms, and the churches report to the schools the names of children released from public schools who fail to report for religious instruction.
As you can see, the religious institutions take attendance and report it to the school. This makes the church an agent of the public school, an unwise position for a church in my opinion.
I appreciate what is said in the dissent by Justice Jackson:
No one suggests that the Constitution would permit the State directly to require this "released" time to be spent "under the control of a duly constituted religious body." This program accomplishes that forbidden result by indirection. If public education were taking so much of the pupils' time as to injure the public or the students' welfare by encroaching upon their religious opportunity, simply shortening everyone's school day would facilitate voluntary and optional attendance at Church classes. But that suggestion is rejected upon the ground that, if they are made free, many students will not go to the Church. Hence, they must be deprived of freedom for this period, with Church attendance put to them as one of the two permissible ways of using it.
The greater effectiveness of this system over voluntary attendance after school hours is due to the truant officer who, if the youngster fails to go to the Church school, dogs him back to the public school room. Here schooling is more or less suspended during the "released time" so the nonreligious attendants will not forge ahead of the churchgoing absentees. But it serves as a temporary jail for a pupil who will not go to Church. It takes more subtlety of mind than I possess to deny that this is governmental constraint in support of religion. It is as unconstitutional, in my view, when exerted by indirection as when exercised forthrightly.
As one whose children, as a matter of free choice, have been sent to privately supported Church schools, I may challenge the Court's suggestion that opposition to this plan can only be anti-religious, atheistic, or agnostic. My evangelistic brethren confuse an objection to compulsion with an objection to religion. It is possible to hold a faith with enough confidence to believe that what should be rendered to God does not need to be decided and collected by Caesar.
As a Baptist, I believe that Zorach v Clauson was wrongly decided. I hope that no Baptist churches would enter into such a scheme, since (in my considered opinion) it uses subtle force to prod attendance for religious instruction. If I were a parent, I would NOT want my child to be taught by a church that doesn't believe that the message they present could not get an audience without the government's help.
The USA Today opinion piece promotes this scheme because they claim parents want moral and character-building education for their children. While discipleship to Jesus (not just religious instruction) provides moral and character growth, morality and character is not the gospel of Jesus. If you want moral and character formation, there are many programs, such as Scouting, that directly tackle those issues. But discipleship to Jesus is FAR deeper than that, and Jesus doesn't need Caesar's help to do His work.