Gender stereotyping is a vicious cycle (multiple cycles even) and definitelly goes through both genders.
Mind you, in my experience it does have some cultural component to how far it goes, but even in the most gender-egalitarian country I lived in (The Netherlands) there were still plenty such expectations and, for example, before the remote working era the percentage of couples there with a huisman (the male version of housewife) was only 18%.







Whilst I’m not sure about contractors specifically, at least in my technical area “Software Development” having the expertise/insight in the social domain (which is not part of the expertise required for the job) to do things like that is more the exception than the rule.
But, yeah, totally agree that the wise, well-rounded and (IMHO) competent professional would at the very least do a bit of subtle “social discovery” to try and figure out who is the best person the interface with.