How can an intense desire for righteousness put you at odd with the world?
To truly hunger and thirst for righteousness we must completely forsake the worlds version and ideals of self satisfaction (gratification), success and happiness. We must first seek out God and His kingdom. By doing so, you will be ridiculed and mocked by the non believers in the world.
What sort of righteouness is Jesus talking about?
The righteousness that comes from Jesus and walking in his word; the desire to do what is right without compromise.
What promise are we given in this Beatitude?
We are promised that we will receive righteousness, but we must have a true change of heart in order to receive and true desire and thirst for it.