I think it can be likened to the domineering spirit of Jezebel.
Rev_2:20 Notwithstanding I have a few things against thee, because thou sufferest that woman Jezebel, which calleth herself a prophetess, to teach and to seduce my servants to commit fornication, and to eat things sacrificed unto idols.
Who was this woman, Jezebel, who was allowed to operate in the context of the church at Thyatira? In the old covenant King Ahab married a woman named Jezebel who was the daughter of the king of Sidon. She was an evil woman who encouraged idolatry and immorality (Catholic church encourages these, too), and "killed the prophets of the Lord" (I Kings 18:4). Yes, and the RCC also kills the "servants of the Lord". Her name became a proverbial name for feminine wickedness. A domineering, evil woman is often referred to as "a Jezebel" to this very day. Whether there was actually a woman with the name Jezebel living there in Thyatira, or whether this is the name by which she is designated because of her actions, we cannot be certain. Not many families have named their daughters Jezebel since the time of the Old Testament. What we can be sure of is that a particular woman there in Thyatira claimed to be a "prophetess" and was teaching and leading Christians astray unto immorality and idolatry, just like the Jezebel of old. Jesus may be talking about an actual woman here, or the spirit of Jezebel. In any case, His point is well taken.
It is no secret that the RCC turns a "blind eye" to fornication and immorality. Just go to confession and everything will be alright.
Rev 2:24 But unto you I say, and unto the rest in Thyatira, as many as have not this doctrine, and which have not known the depths of Satan, as they speak; I will put upon you none other burden.
Whatever Jezebellian religion was it apparently had been labeled as "the deep things of Satan" by those involved in it. Have you ever noticed how the Catholic Church puts on the pretense of being "mysterious" and "deep"? It seeks to make itself "special" over and above all other earthly religions and it appeals to men's desire for their natural quest for knowledge. These "deep things" or deep musings of the human mind are more often than not of Satan and not God. God has made His "good news" simple in the person of Jesus Christ. It is religion that seduces men promising knowledge of spiritual secrets. I mean, just look at how a billion people have been seduced by the doctrine of "transubstantiation". The "deep things" of God, turning bread into the actual body of Jesus Christ and wine into His blood. Even in non-Catholic circles I have seen the error of "Gnosticism", which is satanically inspired. You know, the pursuit of "deep things", that are in ADDITION to Jesus Christ, Himself.
The spirit of Jezebel is not confined to the RCC, but is very strong there, nonetheless.