Where we used to live, the choices in our borough would have been two failing single sex schools (closest and most likely); two highly successful and exclusive single sex schools (quite local but a very small catchment area, didn't include us); a mixed non faith schools (but tricky to get to and into because of distance). Further afield, but with different catchments, there were the (mixed) catholic and CoE schools (one of each and busable) and then two grammar schools, very nasty journey, plus, guess what single sex and religious.
So as a family that don't like single sex schools, and wouldn't touch a religious school with a bargepole, basically no choice at all.
However, we moved to Canada, where in our town you do go to the local primary (automatic admission) although you can choose to go elsewhere, few people do (there are elementary schools offering Montessori, French Immersion, Science or Arts specialisations). At secondary level there are three schools, which again have automatic entry. All the schools have excellent results, and I have yet to hear anyone complain about the school their children attend, or worry about entry at elementary or high school.
There are two private church schools, but they are seriously religious, and require parental volunteerism as well as regular attendance and priestly sign off. Very much a minority choice.
My view is that all selective schools are divisive by nature (how can they not be), but I would include single sex, grammars and independent schools in the debate.