It's not a 'dogma' to expect that the education of children should be evidence-based! Investigations into what's termed 'spiritual practice' and studies of faith traditions contextualised within a history curriculum are welcome. But religious worship should surely be a private family affair, not something underwritten by a democratic state, as it is a claim to 'understanding' that simply doesn't yield to evidence. Teaching children that God exists is no different to teaching them that God doesn't exist.
Faith schools, as you imply, are a hangover from the fact that when the mass education system was properly instituted in 1944, much of the school estate was owned by churches, so their conceits had to be accommodated. If you were to design education now, given the non-religious majority in this country, you certainly wouldn't think it a good idea to create division among children by allowing faith schools. To remind you, there are no Muslim children, or Catholic children - there are just children.