This is a good question. There are several types of conflict in the movie.
The most obvious type of conflict that is explored is based on the genetic make up of a person. Those who are genetically "perfect" are on the one side, and there is everybody else. This creates a caste system, where causes a lot of tension and conflict in society.
Conflict is also explored through personal relationships. For example, when Irene finds out that Vincent is not the person he says to be, what will she do? There is inner turmoil.
There is also personal conflict. Will a person fight to overcome his/her genetic makeup?