I have been doing FlyLady for a couple of years and consider myself to be a Feminist.
To be honest, when you initially read the emails, it does look like a housewifey sort of site where the little woman is expected to clean up after her man but the more I have gotten to "know" her the less true that seems.
FlyLady was, years ago in an emotionally abusive marriage. I have seen posts where a wife writes in to complain about her husbands expectations and where she has been told not to tolerate any such treatment from a husband.
FLY = Finally Loving Yourself. The first rule of the day is, before you look after the house, look after yourself. Brush you hair, get dressed, put on make-up, be ready to face the world. I have also seen her say to women who object to putting on make-up "Well then, just moisturise!" Also built into the routines are things like drinking water and taking exercise. The idea is to take care of you, first and foremost.
She is not keen on Perfectionism. She does not advocate a perfect house, just a house where you feel happy and comfortable and where you don't isolate yourself because you are too ashamed to have anyone over.
She does advocate a relaxed attitude to cleaning and housework. Most of it does not involve mad cleaning sprees involving skips. It's a little and often approach which means that you don't wear yourself out, and she does build in time for coffee breaks! Everything is done in 15 minute steps, after that you stop, whether the job is done or not. The next time you tackle it, you do another 15 minutes and so on.
Personally growing up, I had no guidance as to how housework should be done. My mother is a hoarder. My father did his best but anyone who has ever lived with my mother usually gives up because her hoarding and disorganisation actually prevent other people from cleaning.
Last year, I was in her house and found an unfinished cardigan which she had long since stopped knitting. I told her we should throw it out and she wouldn't. I asked her why and she said she might finish it if she could manage to buy the right wool. I then asked how long she had been knitting it and she said, before I was born! I am 42!!! If I didn't have FlyLady, that would be me!
I just ignore any God references and fit it in around my own job and kids.
Dh doesn't follow it but does a big clean up with the boys on Saturday. He is naturally better at cleaning than me so doesn't need a system.