Scripture indicates that the contemporary religious structure when Christ was here in the flesh, was contrary to His teachings on several issues. He was, and I'm using the past tense for pedagogical reasons, hence this is about the period He was amongst us in person, acting notoriously radical, and, was harshly criticizing the conservatives of that time.
As for semantics, what I believe we need to focus on, is His Grace and not so much for whether He was conservative or not. As somebody's pointed out, the Gospel is key.