Blaine amendments were passed in the 1880’s. Im sure they were fought against and lost.
You are correct about NJ, It does not have a blaine amendment. Its one of 11 states that don’t have it.
In the 1960’s they tried to repeal New Yorks Blaine amenement and it had something to do with the wording forcing an entire re-write of New Yorks constiotution.
That’s why New York actually provides a lot of indirect aid to parochial schools like bussing and books and computers that was found to be legal.