my parents and most of their friends belonged to CFM in the 50s and 60s. the leadership of CFM split after Humanae Vitae was proclaimed in 1968 over the issue of birth control and the church’s reiteration of that teaching. Some of its leaders had been consulted by the Vatican team that researched the issue and made its recommendations to Pope Paul 6, and there was a widespread expectation (or wishful thinking) that he would soften the stance against ABC. That of course did not happen, and a lot of disillusioned people left the movement. In our home parish, CFM was in disarray, and about half the families involved eventually left the church, at least for a time.
Had no idea it was still active, but I would make sure its leadership and members were orthodox in their views and Catholic practice before joining.