Rule Utilitarianism says that we need to stick to at least some rigid rules to promote the most happiness or preferably the minimisation of suffering.  Ending suffering is more vital than improving happiness.  It fears the simple version of utilitarianism that you do whatever makes the most happy can be abused and backfire.

It says that rules are necessary even if they cause a lot of unhappiness in individual situations as long as the general happiness is maintained or heightened. That is why things like lying and stealing are only allowed under certain circumstances for serious reasons. But when you are forced to do them by the circumstances they are not lying and stealing. Are you a liar if your mouth takes a mind of its own and lies? You are not a liar when forced by your circumstances either. Are you are thief if you have to steal to save a life? And if you need to take something that belongs to another for a serious reason then it is no longer that person’s for ownership is just about order. Nobody really owns anything when it comes to such cases. Everything belongs to everybody in a sense.

Rule Utilitarianism recognises that certain rules are more conducive to happiness in the long run than others and that is how it works out its rules. This avoids the danger of having a morality that leads to too much freedom like classical Utilitarianism.

Does Rule Utilitarianism give no reason to disapprove of secret stealing from a shop or employer within reason and slander and discreet adultery or child-abuse and many other things we detest? Secret wrongdoing makes people sad for they know it is going on though they cannot prove it or they know how likely it is to happen to them so it is wrong. Even if it never happens it will still make people sad for they just do not know so one might as well do the detested things. But it will make them sadder if it is accepted and not preached against for they will be more cynical.
Here are some rules,

Don’t tell lies when they lead to more lies for you will then get caught and lies destroy trust and we would never know if a person is telling us the truth perhaps for a good reason.

Don’t break up families with young children for it is better for reasonable families to stick together.

Don’t let religious belief thrive for it is something extra to bother people and for them to fight over and any good benefits can be gained by spirituality without religion.

Rule Utilitarianism is not perfect but if it is the best we can come up with we have to follow it.

Another thing that seems to be wrong is that it cannot lay down general laws that the world can accept. What laws we have has to depend on what the majority of people want and like. It seems that if most people want to rape it has to be legalised and it is right to rape if Rule Utilitarianism is true. Such a system will serve only to put up walls between nations and races and we know how much trouble division causes. The law could let x number of men with strong passions to rape some women to curtail much of the harm. To answer that rape is wrong even then is to deny the Utilitarianism of Rule Utilitarianism. You may reply that the women will be unhappier and general happiness will be minimised. But what if this were not true? Rule Utilitarianism has to stand for the view that as long as rules make us happy it does not matter what they are.
It is no refutation to say that women and people being happy in a world where rape is allowed and encouraged will never happen. That is beside the point.
Since the person is an absolute value the desire to rape would be a sickness and would have to be cured instead of practiced. But to say that the person is the absolute value or is the most important thing is to deny Rule Utilitarianism.
People generally agree on what is right and wrong or on what they want to be right and wrong. They often have serious intellectual difficulties with some of the principles. It is the particulars that may cause the problems but they are not that serious.

If people won't accept the rules that are good for them then the theory has to advocate forcing them to obey them.
If most people break the rules then the rules only cause trouble by being kept in force for they cause dissent and guilt. This suggests that Rule Utilitarianism has to get more lax the more people offend.

If people won’t keep the rules well, their belief in them will only reduce their happiness or increase their suffering through pangs of conscience and shame. But that is no justification for refusing to believe in the rules for it would be worse if you did not if they are right. It is not the rules that hurt you but your not keeping them.

Some say, “Rule Utilitarianism says that what we feel should determine what we want to make right and wrong and not what reason says. But people who do not take their instructions from reason but emotion have no right to make laws. They are forcing their feelings about what is right and not what is right on other people. Rule Utilitarianism is rubbish.” But if reason tells us that it has to be feelings we must listen to for there is nothing else the theory is vindicated against this accusation.  It is not wrong if it is a necessary unavoidable evil.

Some would object to Rule Utilitarianism on the grounds that I am most sure I exist therefore nobody has the right to force these rules on me. But the egoists have to go along with the majority for the sake of their own welfare anyway. Egoists know they might not be alive if it were not for rules.

Humanists should believe in Rule Utilitarianism as the best of a bad lot.