As for data support, look at the primary voting data. Most evangelicals voted for someone else during the primaries until the very end.

That’s most likely true. Remember most evangelicals voted against Trump in the primaries. And a great many of them held their nose and voted for Trump when it was clear he was the only alternative to Clinton. Furthermore, “evangelical” is a pretty broad term that relies on self-identification and no definition.

None of this information answers my questions.

“It is settled law that the Constitution entrusts the conduct of foreign relations exclusively
to the Executive Branch, as it makes the President “the sole organ of the federal government in
the field of international relations.” United States v. Curtiss-Wright Export Corp., 299 U.S. 304,
320 (1936); see also Chicago & S. Air Lines, Inc. v. Waterman S.S. Corp., 333 U.S. 103, 109
(1948) (“The President also possesses in his own right certain powers conferred by the
Constitution on him as … the Nation’s organ in foreign affairs.”). In keeping with Supreme
Court precedent, the Executive Branch has consistently taken the position, across administrations of both political patiies, that the President has exclusive authority to conduct diplomacy with foreign nations.”

“With all respect, the Constitution assigns the President the role of charting the course of U.S. foreign policy and detetmining which diplomatic communications advance the national interest. Policy disagreements with the President’s decisions on those matters do not create a legislative right to review the President’s diplomatic communications with foreign leaders”

Source https://assets.documentcloud.org/documents/5777433/Cipollone-Putin.pdf

What was “fake” about Trump keeping his meetings with Putin secret? or how Trump made excuses for Putin’s behaviour?