Ok, let's take a case study. Outer London borough. Three closest schools are faith schools. The closest non-faith schools have tiny catchments as a result because of the number of kids coming from further schools for the "desirable" schools.
When a child fails to get into any local schools, the one they're offered is a 30 minute drive away (as opposed to a short walk). Ironically, it's also a CofE school. So where's the choice?
("Fortunately" in our case, one of the local CofE schools had a less-than-stellar Ofsted and suddenly a lot of people who were dead set on faith education suddenly found they had other priorities, so there were places available.)
On to your wider point: I can hold two positions in my head at once. I can believe that the state should not fund faith schools, and also believe that if the state is going to fund faith schools (as it does), then state money should not be used to discriminate in school admissions and that all children should be treated equally in the question of access to state schools.
As you've said, plenty of under-subscribed faith schools don't use any selection criteria or filter as they don't have enough applicants.
Segregation by religion is a fact - particularly in Catholic schools where up to 100% of the intake can be selectively Roman Catholic children - what else do you call it when a school is entirely of one faith, regardless of the religious makeup of the community they live in?
This is less so for most CofE schools where the 50% rule applies. But any schools that apply selective criteria, including on faith, are ensuring a school population that is of a higher socioeconomic status overall than its surrounding community. So we're segregating by wealth.
Your posts demonstrate that you are arguing from a position of feeling rather than fact. It's unfortunate for you that the facts about the education system don't support the position your feelings think they should.