Modern people are typically nihilist, yet do not behave as nihilists - rather they are intensely (albeit selectively and in an unbalanced fashion) concerned with moral issues.
They are relativists who do not believe in the reality of reality, believe that life is merely about pleasure - yet they are altruistic, kind, passionate about (some kinds of) injustice and so on.
How is it possible to live in such a state of obvious contradiction?
What makes this paradoxical state possible is, I think, pride.
Pride is highly valued and positively encouraged in modern society - under names such as self-esteem, and in processes such as self-development.
Much of modern education, 'therapy', self-help, lifestyle journalism etc is about making people 'feel better about themselves' - i.e. pride.
People therefore believe contradictory things because they feel themselves superior to the need for consistency, indeed inconsistency is evidence of their superiority.
For example, a person with nihilistic beliefs, one who thinks all behaviour is a contingent result of blind evolution, may behave altruistically - and doing this makes him feel good about himself:
'Look at me, I believe in nothing, I could be utterly selfish and short-termist - and yet I do these good things - how impressive is that?!'
Modern man is therefore his own Nietzschian hero of self-will; he sees himself as creating his own system of meanings, values and purposes by the sheer strength of his own mind.
'I did it my way' is the favourite song of the modern world.
Each individual consumed in self-worship, constantly amazed at his own remarkable ability to defy logic, to shape the world to his own desire; to hold himself suspended above the void of his own nihilism by the sheer strength of his own pride...