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The Wikipedia article on Egyptian Temples has a rough estimate as to when the last temple of the Old Egyptian Religion, The Temple of Isis at Philae, was closed - as early as 456 if one goes by inscriptions found at the site, or as late as 535, if one believes Procopious. They source the claim from the 2011 edition of The Archaeology of Late Antique Paganism, which argues a gradual and organic decline that culminated in the abandonment of cult activities well before the hard cut-off of Justinian's command to destroy the temple. While cult activities may have continued in isolation, this is the end of the Old Egyptian Religion in recorded history.
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Overall worship of Egyptian polytheism began around 2,500 BC and began it's decline around the late 4th and 5th Centuries CE as Christianity became popular, and was finally disposed in the 6th. When Christiandom came to Rome it spread early across the Mediterranian. Christian Roman Emporer's outlawed "Paganistic" teachings and cults.
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Christianity became the official religion of Rome under Constantine (306-337 AD). Soon after that there were major doctrinal disputes between the Bishops of Alexandria that had to be arbitrated between his sons. So by 350 AD at the latest you'd have to say Christianity was well established.
Of course, long before that Greek and Roman influence might have replaced Amon Ra.