I think you will find the public will learn the opposite of what you want: This is an example to progressives that they too in some situation have the power to send strong signals about standards expected of those who expect to be in leadership positions - even in private companies.

This has been the case "forever" for moralists on the right, from long before McCarthy. Try to become a politician or high level exec in the US while showcasing features of your personal life that does not fit into a relatively conservative, Christian narrative. Your odds just became vastly worse.

This is one in a short, but growing, set of examples of situations where people have been successfully ousted for supporting relatively mainstream but still bigoted viewpoints.