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Is it only Roman Catholicism that teaches the possibility of universal vulnerability of demon possession?
Is this teaching specific to Western (Latin Rite) Catholics or do Eastern Catholic traditions teach the same universal vulnerability?
Are there any other Christian traditions that teach this same universal vulnerability?
The answer to the first question is no.
The answer to the second question is yes.
Now let me explain.
According to Catholicism, this is a universal doctrine that applies to the whole Church. A Church divided on doctrine can not stand. The only things that differ in this matter are the rules for the application of official exorcism. The Catholic Eastern Rite rules of exorcisms are to be found in the Eastern Rite Code of Canon Law (Codex canonum ecclesiarum orientalium). Thus the only difference between these Rites is not Catholic doctrine or teachings, but in the application of rules governing the application of the sacraments and sacramentals.
It could be noted that in my response to the question: (According to Catholicism, does reception of the gift of the Holy Spirit protect against demon possession?) mentioned by the OP that as a title of example I stated that Saint Mary of Jesus Crucified had been possessed by demons twice and that the last on was for 40 days. Now Saint Mary of Jesus Crucified was in fact a Catholic nun of the Melkite Greek Rite Catholic Church. She was not a Roman Catholic.
As for the second part of this question, there are some other denominations that teach that all of mankind could be susceptible to a demonic possession.
The Orthodox Churches perform exorcism on their own faithful, when necessary. Each denomination believes they hold the deposit of the true faith.
If a particular denomination performs valid exorcisms on their own faithful, it follows logically that possession for mankind is a vulnerability of every individual on earth.
The monks from Russian Valaam monastery consider that everyone is possessed at some level, depending how much they are burdened by passions, so they recommend living according to God’s commandments: fast, prayers, confession, repentance and Holy Communion.” - The Secrets of Orthodox Exorcists
Lutheranism holds the possibility of possession can afflict anyone.
The Lutheran Church traces the practice of exorcism to the Scriptural claim that Jesus Christ expelled demons with a simple command (Mark 1:23–26; 9:14–29; Luke 11:14–26). The apostles continued the practice with the power and in the name of Jesus (Matthew 10:1; Acts 19:11–16).[8] Contrary to some denominations of Christianity, Lutheranism affirms that the individual, both the believer and the non-believer, can be plagued by demons, based on several arguments, including the one that "just as a believer, whom Jesus Christ has delivered from sin (Romans 6:18), can still be bound by sin in his life, so he can still be bound by a demon in his life." - Exorcism in Christianity
In the Pentecostal Churches tend to believe that a "spirit-filled Christian" cannot be possessed, based on their beliefs.
Yet grievous sin against God are always possible post conversion and baptism of all believers whether Catholic, Orthodox, Lutheran Anglican or Protestant. All must work with Divine Graces accorded to every individual believer regardless of denomination.
In the Pentecostal Church, Charismatic Movement, and other the less formalized sections of Christianity, the exorcism ritual can take many forms and belief structures. The most common of these is the deliverance ceremony. Deliverance differs from the exorcism ceremony in that the Devil may have gotten a foothold into a person's life rather than gaining complete control . If complete control has been gained, a full-fledged exorcism is necessary. However, a "spirit-filled Christian" cannot be possessed, based on their beliefs. Within this belief structure, the reasons for the devil to get a foothold are usually explained to be some sort of deviation from theological doctrine or because of pre-conversion activities (like dealing with the occult). - Exorcism in Christianity