“The benefit of the public is how it raises Hashem’s glory in their eyes.
If it doesn’t, then obviously you gotta do what you gotta do, but there is no ברוך אלקי שמעון there.”
If you shecht an animal, do kaporas with a chicken, do metitza b’peh or even a simple bris mila or you exclude women from various religious leadership positions or you make a Brocha loud and clear, even in public, of shelo asani isha, you’re making a Kiddish Hashem because the public sees you’re doing what Hashem told you to do. Even if it is unpopular, in contemporary times, among some or even most gentiles and secularists.
Avrohom Avinu made a Kiddish Hashem by the akeida even though popular opinion may have considered him to be an attempted murderer.
Simply because in all of the above examples, and in many others, the person followed Hashem’s command and the public saw that. Even if the public opinion is opposed to following that command of Hashem.