If you look at my definitions of the terms, you will see that we seem to have different definitions of the word yeshivish (which is logical- I seem to be coming from a less yeshivish mindset than you are.) I know Breuer’s pretty well- I have close relatives there- and the school is absolutely yeshivish. Not as yeshivish as BYM or BYR, but definitely yeshivish in ideology, specifically compared to Ateres, MHS and Bruriah.
I defined yeshivishness generally by the hanhala. If there was a disparity between hanhala and students, I noted it.
The majority of the people I know of who go to BYM (and I live in a yeshivish enough neighborhood that the majority of the people on my block go there) are very yeshivish. Their parents are in chinuch or other klei kodesh and they will go on to BJJ, Hadar, Nachlas, Bnos Sara, etc (just a few people have gone to off the top of my head). For years BYM was known as “the most yeshivish” of the Monsey high schools. BYR is working hard to catch up. My mom went to BYM when it was a community school- chassidish girls as well as girls in pants. No uniform, just a dress code. That’s a community school. BYM is definitely yeshivish. Yes, Breuer’s is as well.
Student body wise, the schools are definitely a mix. 100% true. But each school still has a certain character.
While I personally didn’t go to a Monsey high school, I grew up here, still (basically) live here, and have siblings and friends who have gone to the schools being discussed. I’m not pulling this out of a hat.