Would the Catholic Church school system meet the criteria for being “imbued with a specific denomination’s religious worldview”? If so, is that where you would send your children, or were you opposed to a specific denomination’s worldview”?
I don’t believe there is a problem with an education that is beyond a specific denomination.
The only way to avoid any non-neutrality in the content of what children are taught is to have the children taught by robots. You probably support parents doing the teaching, but that is only acceptable if we assume that the parents have the perfect knowledge of true religion. Otherwise, you have muslim parents teaching their faith to children, which hardly seems superior to the agnostic teachings of a typical public school.