"To perceive the conflict" means to understand or become aware of a disagreement or problem that exists between two or more people or groups. Full definition
Why might teachers perceive a conflict between standards - based teaching and differentiation? (ascd.org)
Because of an identified real or perceived conflict with national law. (law.stackexchange.com)
The threshold test of perceived conflict in legal matters is much higher than say helping competing companies implement an enterprise software system. (remakinglawfirms.com)