I think you have it backwards. Abolishing prayer in school is not authoritarianism and doesn’t reduce personal freedom. You’re still free to pray on your own at school. Having an official religion is authoritarian (unless it’s a religious school), and pressuring people to participate in a prayer is pressuring them to have less personal freedom (from your religion).

I guess authoritarians tend to view a policy which gives equal preference to everyone as an attack on their “special status” and a reduction of their freedoms.