Of course they should. When the government funds schools and requires that kids up to a certain age have schools available, the government can insure that the schools are teaching certain minimum things to all children. Catholic doctrine has nothing to do with secular schooling. Evangelical views have nothing to do with secular schooling. If you want your kid to get a religious education, too, then send him/her to Sunday school at your chosen church. A government funded school is to teach reading and writing contemporary English and basic math, history, and science, etc., not religious values.
I'm pretty old now, but in my day, the purpose of secular school was to learn to be an educated citizen capable of reading, writing, basic practical math and science, and critical thinking and reason. The purpose of religious school was to learn to be a Jew, Catholic, Protestant Methodist, Presbyterian, Unitarian Universalist, etc., and make some kind of commitment. Nobody at the secular school had to meet some arbitrary religious requirements, but they had to meet secular requirements for teaching the subject or with small kids the age grade intellectual material and public decency standards.
Government doesn't fill schools full of propaganda - religious schools do.