Carter was an ideological animal. I don't assume that he was the brains. He was only animated from his twisted illogical liberal mindset, but his men and specifically Brzezinski knew damn well what he was doing. This was a leftist conspiracy to make up for their supposed "wrong" of the CIA by "installing" the Shah as well as protect ME from communist expansion. Look what they have done to the world now? If you read between the leftists' lines specially their elite journalists, they pretty much concede it ....begrudgingly.
There's two things there. One was guilt about the CIA's actions in the fifties. The other was a desire to head off the Soviets.
I don't doubt that Carter's people felt that kind of guilt and didn't back up the Shah to the degree that they could have. Whether they really wanted the mullahs to rule is another matter.
If you saw all the protests of "Iranian students" in the West, it didn't look like most of them expected the kind of Islamicist regime they got. If they were that blind, I doubt Carter and Vance had much more insight.
According to Wikipedia (a doubtful source to be sure, but convenient) Brzezinski supported the Shah to an end and even favored US military action to keep the Shah in power. If Carter overrode him I suspect it was more because of mushy-headed idealism or guilt than any plan to bring the Ayatollah to power.
The other motivation -- keeping the Soviets and Communists out -- was shared by people across a broad spectrum of political opinion. Republicans and Democrats, for example, both supported the Afghanistan resistance, which became a breeding ground for radical Islam.
It seemed like a good idea at the time, I guess. Whether it really was for the best depends on what happens in the future. In any case, however screwed up Carter's views have been over the years, if it was a wrong headed policy, the guilt goes far beyond Carter and his team.
You can certainly attribute blame for what happened to Carter as well as to the Iranians involved, but I suspect the results were more a result of his not having a clue as to what would happen than of his having a conscious plan to achieve what actually resulted.
It's not that I'm defending Carter's incompetence, I just don't see any master plan to mess things up.