Delatron
I don't think it's a case that being a SAHP Vs working full time is or isn't perpetuating sexism.
It's totally possible to support families to structure their parenting and working roles in a way that works for them, whilst also being willing (like you have) to critique the society that is inherently sexist.
The waters get muddied when people confuse being a SAHP and being a housewife. More women than men become SAHP for a range of complex reasons, but having a SAHP isn't inherently sexist.
Adult A deciding they don't want to work, that female adults who work are on the hamster wheel and have drunk the KOOL aid, whilst relying on Adult B who is working hard to fund a lifestyle that enables Adult A to live a lifestyle of leisure, do some volunteering, have hobby time, and do the housework is going to ruffle feathers because Adult A can only have the sort of lifestyle they want because Adult B is working to fund it all. This sort of situation would be branded cocklodging if Adult A was a man, but if Adult A is a woman it gets called being a housewife and then the same old sexist tropes come out about how it's so important for husband to come home and not trouble himself with housework, the housewife does all the domestic stuff so that the husband isn't stressed by a messy home when he comes in, that non housewife women can't possibly have a home that is as nice or as tidy as a housewife, that only housewives have the time to cook proper meals because they have prioritised time over money for handbags (and other misogynistic ideas that women working out the home are only working for petty cash to fund expensive and frivolous shopping).
Then there's the claims that the women who work outside the home are mugs because they end up doing more chores anyway etc (note that on this point, it's more misogyny because it suggests that being a housewife and doing all the cleaning is great and liberating, and the problem apparently lies with working women, rather than men stepping up and doing their fair share).
A lot of the housewife rhetoric tends to boil down to sexist stereotypes where the priority is catering to men who don't want to pick up a dishcloth.