It used to be that Catholicism was a mandatory subject at public schools in many Catholic countries such as Spain and Italy, and even today some form of "cultural Catholicism" is mandatory in the public school systems of many Catholic countries in Europe and Latin America (especially in Italy, where crucifixes remain mandatory in school rooms).
In my country, the Philippines, the educational system is basically secular and sometimes a tad anticlerical or (more frequently) immoral, but it is not essentially hostile to Catholicism. The lack of religious education is not due to proscription but due to the fact that we have very, very few lay catechists and almost no priests and nuns engaged in teaching public school children. Nevertheless, it is common for Catholic prayers to be publicly recited by teachers and administrators in public schools (even in predominantly Muslim areas!), for images of Our Lord, of the Blessed Virgin Mary and of the saints to be prominently displayed in public schools and government buildings, and for important events in public schools to be celebrated with the Holy Mass.
I do not see how Catholics can be supportive of Catholic traditions being kept alive and well in the public school systems of Catholic countries, and yet be so hostile to the idea of Orthodoxy being taught in the public school systems of -- surprise, surprise -- Orthodox countries. Let's not be hypocrites. Or, to be consistent, we should oppose all religious education in public schools, period. Sad to say, this latter position is something I hardly find compatible with Catholicism.