Asking "whether the woman was a housewife, why she wasn't working, and where she got her income from" seems perfectly reasonable if they were trying to offer car finance, in fact not asking questions to figure out whether the person could afford the payments would be a dereliction of duty.
"Are you a housewife" is relevant because as far as I remember every credit application has required me to say what my job is, and many SAHP (or SAH non-P) prefer to consider themselves a "housewife" over "unemployed".
"Why aren't you working" is relevant. Someone who doesn't work because they are married to a high earner and doesn't need to will be a different risk to someone who isn't working because they are on disability benefits. Are they not working through choice or circumstance? The key is, is the loan affordable.
"Where do you get your money from" is relevant because if someone has no job those who offer credit are expected to do due diligence to ensure (for example) they are not being used to launder money. There are lots of valid reasons why a person might have money but not earn it (partner in a highly paid job, inheritance, trust fund, lottery winner) but the person offering credit needs to understand where it's coming from.
YANBU to challenge sexism but YABU to do it without considering rational explanations first. A builder talking about a "minger" is obviously sexist. The garage example certainly isn't.
I suppose your real decision is whether you feel more comfortable challenging things but being made to realise you were an idiot, or not challenging things and wishing you had?
BTW, overhearing part of a conversation is a great way to get the wrong end of the stick.