You wrote:
“What in God’s Holy Name does Rome and Canterbury have in common?”
History. At least from the 6th century until about 1534. Anglican churches will either become Catholic again or they will become mosques.
Exactly. “Be England thy dowry as in days of Yore”
They know this which is why there is so much hostility.
That is history long gone. Whatever similarities there were, they no longer exist. Yes, I know that there are groups within the Anglican community, such as the Anglo-Catholics, that see themselves in doctrinal agreement with Rome, but they are a minority. I went to graduate school in England, and I lived in an Anglican college. Despite my love of the Anglican liturgy and the beauty of their churches, I found nearly all the Anglican priests to be apostates.