The difference is that utilitarianism has no defined boundaries, while many religions like Catholicism do.
Catholicism teaches that it is never moral to take another’s life unless it is the minimum response necessary for self-defense. Even then, conditions still apply. If you are going to kill a political leader that has been doing crimes serious enough to warrant his or her assassination, you still need to have a plan of how to stabilize the country afterward. You can’t just kill him or her and let the country fall into chaos. There are many more examples like this.
The above is only an example of a more general approach. Catholicism and several other religions provide clear guidelines on what is moral, how to factor in special conditions, the steps that need to be taken to ensure justice, etc. In a confusing world, these guidelines are necessary to keep things in bounds.
Utilitarianism, on the other hand, does not have these bounds. There is a general principal of “greatest happiness for the greatest number of people,” but no absolute guidelines on how to put this into effect. It is impossible to fully gauge the full effects of any one action (would you run a poll before every action?). Furthermore, “happiness” cannot be easily defined for the masses (most Germans were happy with Hitler, even to the bitter end).
All of these ambiguities in utilitarianism mean that utilitarianism is not a stable foundation for society. You yourself said that your moral opposition to the Holocaust is only your personal conviction. The German state had a very different opinion. If “all you can do” is try to
convince the German state that
their actions are wrong, you should not be surprised if the German state tries to
convince you that
their actions are right. See where this is going?
Utilitarians think that “the greatest happiness for the greatest amount of people” is in everyone’s self-interest. They think that people will recognize this and will thus try to support their own and everyone else’s happiness. The problem is that happiness is not defined. What if the vast majority of people would receive great happiness by eliminating the small, inferior races? Mathematically, the overall level of happiness may be greater if the “inferior” races are eliminated, due to the larger numbers of the majority doing the ethnic cleansing. Any other issue could be substituted for race and be justified by the mathematical result.
The fundamental problem in utilitarianism is two-fold:
- Happiness is not defined as anything concrete and consistent. It can be understood to be anything.
- By appealing to “greatest happiness for the greatest amount of people” utilitarianism resorts to a mathematical standard. This is not a good standard. Coupled with the ambiguity listed above, anything can be justified with enough popular support and popular desire.