Utilitarianism is a philosophy that values doing the greatest good for the largest number of people. Its concept of general welfare is the well-being (avoiding harm and maximizing benefits) of the masses, in which the majority benefit. However, this does not necessarily take into account certain minorities or individuals.
Someone might object to general welfare of the Utilitarian type if it happened to clash with the welfare of a specific, vulnerable minority. For example, if the best thing for the majority of people was to prevent the spread of a specific, localized disease, according to Utilitarian doctrine the infected individuals should be quarantined and have no interaction with others. This would prevent them from getting any outside help and potentially doom them. It would definitely not benefit those sick individuals. However, as the disease would then be contained, it would be to the benefit of the majority—the "general welfare."
This often comes up against other philosophies, specifically those with strong beliefs about what is "right" and "wrong." For example, some belief systems would say that we are obliged to help sick people, even knowing the risks, because it is the "right" or "moral" thing to do. This is actually more often the case, and people tend to make decisions based on their morals or beliefs, not simply what makes the most utilitarian sense. For a deeper look at this, I suggest the Sheskin and Baumard article linked below, entitled "Switching Away from Utilitarianism: The Limited Role of Utility Calculations in Moral Judgment."