It is possible to be just a little self-righteous and therefore not cause much offense to anyone, people who are too self-righteous may:
Be quick to judge others
Belittle those around them
Be smug
Act condescending
Be narrow-minded
Be intolerant of other people’s faults
Believe that they have the answer for everyone else’s problems
And more...
Meanwhile, self righteous people often have a very hard time being empathetic. They only view the world through their own eyes, and cannot even fathom walking in someone else’s shoes. People who are too self righteous are also too sure of their own opinions. They will stick to them at any cost, and often refuse to hear opposing arguments. They will also never change their opinions based on new information they have received. They also hate to take people's advice.
What often drives excess self righteousness is fear. Fear of the unknown, fear of losing control, fear of realizing you may have been wrong but if you release this fear to tap into your inner ability to let go of negative emotions, you will find that being more open-minded and less judgmental is actually freeing. The method to just shake off the fear and be at peace may also be helpful to your state and well being. To release the need to always be right can make you experience empathy and welcome the thoughts, ideas and opinions of those around you.
Bar advice. No one in the world is right all the time. You're only losing yourself in a world of denial. Anyway, who wants to be around someone like that. Think about it.