They shouldn't exist.
They can also discriminate in their staff selection and promotion.
They change their entry criteria to get the 'right' kids in, RC schools used to not have many ESOL kids, until Polish people started to move tot he UK, suddenly you not only had to be baptised but baptised ASAP after birth and within a year of birth.
Then there is what is taught, as well, outside the RE classes, the language(s) taught, the history or the perspective of history, some subjects may not be available at all and others might be compulsory (Yes I am bitter about spending 3 years learning to cook and clean).
Faith schools also may offer counselling or pastoral care that is faith based. In VI form a student made the mistake of telling a teacher she thought she was pregnant, she was told if she was she could have the baby and stay in VI form but if she had an abortion she had to leave.
I totally understand people wanting their children to share their faith but I think that could be accommodated, maybe have secular schools across the board but with a half or even a full day once a week where children can attend a religious school or the school could provide religious instruction.
I think study of world religions should be a secular subject.
But state religious schools are inspected (more rigorously IMO than secular) and required to comply with certain standards.
Ofsted inspect all schools but faith schools have a separate inspection of their RE done by a member of that faith.