We already have a situation where we can cause harm to innocent people for the general good. It's called taxes.
Since I got modded down for that before, here's a hopefully less controversial example: the penal system. If you decide that your society is going to have a penal system, you know (since the system isn't perfect) that your system will inevitably punish innocent people. You can try to take measures to reduce that, but there's no way you can eliminate it. Nobody would say we shouldn't put a penal system into effect because it is wrong to harm innocent people for the greater good--even though harming innocent people for the greater good is exactly what it will do.
I don't think anyone really objects to hurting innocent people for the greater good. The kind of scenarios that most people object to have other characteristics than just that and it may be worth figuring out what those are and why.
Also, some people (such as Hitler and Stalin) are conventionally held up as examples of the evils of believing that ends justify means, but in fact disavowed utilitarianism just as strongly as their critics.
It seems to me that utilitarianism decides how to act based on what course of action benefits people the most; deciding who counts as people is not itself utilitarian or non-utilitarian.
And even ignoring that, Hitler and Stalin may be valuable as examples because they don't resemble strict utilitarianism, but they do resemble utilitarianism as done by fallible humans. Actual humans who claim that the ends justify the means also try to downplay exactly how bad the end is, and their methods of downplaying that do resemble ideas of Hitler and Stalin.
Another way that a penal system is extremely likely to harm innocents is that the imprisoned person may have been supplying a net benefit to their associates in non-criminal ways, and they can't continue to supply those benefits while in prison. This is especially likely for some of the children of prisoners, even if the prisoners were guilty..
Another month has passed and here is a new rationality quotes thread. The usual rules are: