Their influence has dropped significantly. Historically a Catholic priest would be principle or have unfettered access to children. They would often just arrive

Their influence has dropped significantly. Historically a Catholic priest would be principle or have unfettered access to children. They would often just arrive into classrooms and throw their weight around or physically assault children. That has almost entirely stopped. There are now strict child protection laws. Parents can generally opt their kids out of religious instruction. Church attendance in Ireland has collapsed. The patronage of schools by the churches is mostly now a vestige of the past and will eventually be phased out, then the religious orders now accept that.