No, the US had nothing directly to do with Romero's death. I followed the sequence of events closely during that time. A month or so before he was killed, he called on president Carter not to send arms to the Salvadoran military. Arms sales had been prohibited under Carter's human rights policy, but there was pressure on him to renew them. That sermon was reportedly what sealed his fate. The day after that sermon, the church radio station that broadcast it was bombed. I think it was repaired by the time of his more memorable final sermon a month later, where he called on soldiers not to obey orders to murder peasants. He was killed the next day. Suspicion was that a former colonel, Roberto d'Abuisson was responsible. On his deathbed he confessed to killings, but I don't know if he mentioned Romero. d'Abuisson may have been trained at the School of the Americas (located in Georgia, I believe), and where the more paranoid of Latin American leftists thought Latin American police and soldiers were thought torture techniques by the US military. (Tho kicked out of the Salvadoran military, Roberto was connected to some conservative politicians in the US. Young Americans for Freedom, a conservative campus group at the time, featured him in their magazine.) What appears to have happened was that the SOA *did* train legit armed units that evolved over time into the infamous "death squads" that killed so many.
But Romero was a problem for the US. Here we had the US supplying arms and morally supporting a military that murdered people regularly, while each Sunday Romero's sermon broadcast the names and facts known about those killed, complete with some of the gruesome details. His death, about which some of the clueless US media could not conclude if it came from left or right, removed that problem. The Archbishop would have made a great Old Testament prophet. As noted, he was declared a saint by the Catholic Church a couple of weeks ago.
Finally, as to the US's anti-communism at this time, a conservative intellectual whose name I forgot, wrote an article in which she distinguished between communist tyranny and right wing tyranny. She suggested the the US support the latter, as "moderately repressive" and criticized the Carter administration for its criticism of them. The thesis is that communism is permanent, something a people never escape, while right-wing dictatorships evolve. This produced written guffaws, with comentators wondering if torture by a right-handed person was easier to bear than torture by a lefty. She didn't foresee Lech Walesa in Poland and the events that changed the Soviet bloc, and as it happened the Commies folded before the fascists did. So the medieval notion that communism was eternal damnation far worse in its repression than right-wing dictatorships given that no one ever escapes hell took hold, and we supported regimes that would have put Castro's or the Sandinista's oppression to shame for the latters' relative moderation. For this cockeyed idea, Reagan named her UN ambassador. (Just remembered her name, Jeanne Kirkpatrick.)
In fairness, one must remember how the fifties and McCarthyism affected the US, and how easily it was revived. (My favorite 1950s story: a woman officially changed her last name from Allred to Allgood. Strange that the GOP color is now red.) Politicians actually talked in fear about how leftist Nicaragua was just a 2-3 day drive from the US. The current fear of invasion from Central America has precedent, with much the same usual suspects stoking it.