That is entirely false. "Render unto Caesar..." means basically don't refuse to pay taxes to earthly government, a concept existing in Islam.
In fact, one of the reasons why rulers found it easy to embrace Christianity is precisely because of the concept of Divine Right - while before some ruler held to power through force or threat of force, now there was a divine concept that legitimized his rule. He was no longer a strongman, but someone sanctioned by divine power to rule over the common people and made it a sin to challenge his rule.
Not to mention that later Roman/Byzantine Emperors maintained a principle that their rule over entire Christian world was legitimate because they were viceroys of God on Earth.
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