I was taught math the old way, common core is a relatively new term to me.
That said, I use math daily as I have to problem solve regularly and algorithms and parsing data comes up a lot for me.
I HATED math in school, I never got it. After school and in learning programming I've come up with many of my own ways of solving the math problems that I regularly come across, and lo and behold, many of my methods are quite similar to common core methodologies. I WISH that common core was something they taught when I was growing up, I think it's a much broader and more open approach to teaching math which doesn't rely on memorizing algorithms, rather putting the skills of problem solving into the students' hands.
I don't know all of common core or anything, I have no real need to go back and learn it today, but all of the videos I've watched and papers I've read on it make it sound really appealing to me. I don't have kids nor am I anywhere near the school system, but as a generally educated adult who uses math regularly, the only reason I can see for anyone complaining about it is that they're old and set in their ways. Again though, I am not "in" this fight, so my knowledge of why anyone would ever complain about it is very surface level.
Anyway, I know I'm not the target audience of your thread, but I figured since I've done a fair bit of looking at it I thought I'd share my thoughts. I'll be watching the thread cuz it's something I'm very curious to hear others' thoughts on.