At my company, we are putting various checks in to mitigate sampling error, e.g. flagging A/B tests as potentially erroneous when they terminate at non-integer numbers of weeks. Are we somehow doing feminist philosophy?
In your example of gender differences in observations, the correct solution is to parameterize the gender of the observer. I.e., you'd have o_m(X) and o_f(X). This is no different from parameterizing the time since a visitor hit a website in a conversion experiment - a visitor failing to convert after 3 seconds gives you different information than a visitor failing to convert after 3 days. (In this case you'd have o_t(X) instead of o(X).)
The facts that are inferred do, in fact, represent objective reality. They just may not provide a lot of information on it.