They’re utter nonsense. The Orthodox Church in Russia coexists with many Protestant churches and the Vatican has no power to outlaw evangelism anywhere (except in the Vatican City State).
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However, this raises a much more pressing question, however, why should other Christians be trying to “evangelize” Russian Orthodox and Roman Catholics? These are Christian denominations, contrary to the teachings of some 19th century Restorationists, and so there are no souls to be saved by evangelizing their members - we should be focused on converting members of various non-Christian cults like the Mormons, Jehovah’s Witnesses, Unitarian Universalists, and the atheists and irreligious, and heathens such as Muslims, Hindus, Jains, Buddhists, Confucians and other adherents of the demonic false religions, and not trying to “evangelize” our fellow Nicene Christians.
And frankly if anyone dared try to “convert” Roman Catholics to some random church in the public areas of the Vatican, I would fully support the Vatican arresting them, but alas these days the Vatican has gone from being too aggressive in prior centuries to being too timid when it comes to defending the faith.
Here is a recent video of a misguided “evangelist” accosting an Orthodox priest in Greece, along with his very charitable reactions to her conduct (real video of an actual event):
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