Ssndra Harding discusses this in various places, such as her essay "What is Strong Objectivity".
For example, think about a medical study where subjects are primarily male. Do the results in fact represent "objective reality" for the general population?
Or, using your Bayesian example, consider fields that are disproportionately male, and there are gender differences in the observations o(X) that people make. Do the "facts" that are inferred represent "objective reality"?