In the eyes of popular culture (and in the eyes of many philosophy professors), the essence of utilitarianism is “it’s okay to do bad things for the greater good.” In my mind, that’s not the essence of utilitarianism. The essence is, “doing more good is better than doing less good.”
Utilitarianism is about doing the most good. You don’t do the most good by fretting over weird edge cases where you can harm someone to help other people. You do the most good by picking up massive free wins like donating to effective charities where money does 100x more good than it would if you spent it on yourself.
(Richard Y. Chappell might call this beneficentrism: “the view that promoting the general welfare is deeply important, and should be amongst one’s central life projects.” You can be a beneficentrist without being a utilitarian, but if you’re a utilitarian, you have to be a beneficentrist, and as a utilitarian, being a beneficentrist is much more important than being a “do bad things for the greater good”-ist.)