See here: Saudi-Arabia, Oman, UAE, Philippines, Egypt (military junta), Turkey, etc.
If being friendly with an authoritarian state yields economic or military geographical advantage then that overrides any ideological hang-ups involved.
They attack democracies that they don’t like labeling them autocratic and dictatorships. Then install their military juntas. See numerous examples like Chile, Ethiopia, Iran etc.
Stephen Kinzer has written extensively on this in the book Overthrow:
https://www.amazon.com/Overthrow-Americas-Century-Regime-Cha...
On overthrowing the Iranian democracy and installing the Shah:
https://www.amazon.com/All-Shahs-Men-American-Middle/dp/B00S...?
On the Jakarta Method:
https://en.m.wikipedia.org/wiki/The_Jakarta_Method
https://www.amazon.com/Jakarta-Method-Washingtons-Anticommun...?