I think that the Free School Meal argument is weak to be honest, particularly at primary level.
To claim FSM, no one in the family can be working more than (I think) about 16 hours. If you are a two parent family it is far more likely that at least one of you will be working somewhere approaching full time.
There are likely to be more two parent families in faith schools than in non-faith.
That does not mean that these families are middle class, just that, at least one parent happens to be working.
Generally (perhaps with a few high profile school exceptions) the only admissions criteria for a faith school is that you practise that faith and demonstrate this by attending church. No other hoops to jump, no having to live in a certain area, or be a certain gender, or perform in the 11+.
I really do believe that you do not have to break something that is working well in order to meet the needs of everyone.
We need to concentrate on improving the outcomes of all children at all schools. Otherwise we really don't achieve anything positive at all.