It's entirely different when the teachers and the parents "choose" something like common core.
My kids went to a private school for elementary in the middle of the common core dust up in public schools, so before we enrolled them the one of the first questions we asked about was common core.
They told us they were also adopting the approach but that their teachers had been discussing it for years, had a complete transition plan for how to introduce it at each grade level, transition kids based on what they'd been taught at previous grade levels and how to inform parents about what to expect.
The key was that the teachers and admins, through their own professional expertise, were able to research options to improve how they taught and implement them with the blessing of the parents who choose to send their kids to the school. And it went great.
All of the common core horror stories that I've heard, especially around math, were due to horrible execution after the program was essentially forced on everyone. It's a completely different experience when everyone involved decides, "this is the best way and here's how we're going to do it well" vs "everybody has to do it this way now."
Common core was the main driver of choosing a private school for elementary up to at least 4th grade largely because we wanted a consistent learning experience for our kids in their early developmental years. I didn't want risk politics causing disruption in those early years (ideally ever, but early years are where I have my biggest concerns).
