Faith schools have admissions criteria just like any other school, the difference is that the admissions criteria excludes those DC who's parents lack the time, resources or wherewithal to ensure their DC meet the criteria.
At our school, RC DC must be baptised in an RC church, and not in the year before admission. At a stroke, this rules out anyone who hasn't organised themselves to do this.
Next, the DC have to have a form signed by the priest to say they regularly attend church. Priest will only sign this if DC has a certain number of stamps in their Sunday School book. Again, this rules out anyone who hasn't organised themselves to do this.
Then there is the usual criteria of looked after DC, SEN DC, teachers DC and siblings, all of whom must also meet the above criteria, before any other DC are considered. From memory, our school has about 8 different priority listings in the admissions criteria; I don't think they ever get past number 3 or 4 before all the places are filled (2 form of 30 entry).
My DC's school is very diverse, which I was pleased to see, and all the DC I have met are well-mannered and polite, even at their young ages. Our school is outstanding, and I know from discussions with the teachers that parent support and engagement is extremely high, which also helps the DC do well.
Your MIL may have come to her conclusion based on an entirely different thought process, however faith schools admissions criteria is reviewed and approved by the governors on an annual basis, and any DC's parents could appeal if the governors have not applied the policy correctly.