Not necessarily. Where I grew up St. John Fisher Catholic School had both Catholic children, and middle-class Muslim children who didn’t want their kids to grow up ‘in the ghetto’.

I’m going out on a limb here, but I’m guessing the same isn’t true of the Tauheedul Islam School for Girls, or the Yesodey Hatorah Girls’ Primary School, since its application form specifically says Parents will also need to obtain a supplementary form from the school relating to their commitment to the Charedi Jewish faith which must be signed. Any disputes as to whether a child is Jewish will be settled by reference to the Rabbinate of the Union of Orthodox Hebrew Congregations.

As for your second question, I have known a few teachers with incomprehsible accents but have never heard of any complaints about them. Kids don’t actually care about teachers’ accents because they don’t actually listen to what teachers say anyway.

Also interested in how many teachers do have incomprehensible accents. I presume it’s a non-zero number, given that it seems to be about 20% of doctors, and they have to do way more exams than teachers.