Put simply, they are Pharisees. This term will resonate with other Christians, who understand the reference for what it is.
The Pharisees are depicted in the New Testament as legalists concerned with the fine letter of moral laws. They are also viewed sometimes as hypocrites. Additionally, they are perceived as intolerant persecutors of the early Christian community. Saul of Tarsus was a Pharisee who persecuted Christians before he converted and became Paul.
Skillful reference to Christian Pharisees can convey a short, coded meaning to other Christians of how someone can view conservative Christian voices as fundamentally unfaithful to the spirit of the Gospels.