As in OTL, it would have been close, but IMO Carter would still have won. My reasons for believing this are:
(1) The GOP would still be bitterly divided--it would just be the
other half of it that would be dissatisfied compared to OTL.
(2) Reagan's best states in the primaries were in the West and South. But while he would probably have done better in the popular vote in the West, he could not get any more
electoral votes there than Ford did, for a simple reason--Ford swept the entire West in November (with the single exception of Hawaii, whose multiracial population would probably not be more favorable to Reagan than to Ford). Maybe Reagan defeats Carter in California by six points rather than Ford's two points. Maybe he carries Nevada by seven points instead of Ford's four points.
https://en.wikipedia.org/wiki/United_States_presidential_election,_1976 But that means nothing in the Electoral College. Indeed, there is one western state that Ford very narrowly carried that Reagan might well have lost: Oregon.
https://en.wikipedia.org/wiki/United_States_presidential_election_in_Oregon,_1976 Note that Ford had defeated Reagan in the Oregon primary:
https://en.wikipedia.org/wiki/Republican_Party_presidential_primaries,_1976 Also, Oregon was one of the few states where Eugene McCarthy's vote made the difference, and I can easily see some McCarthy voters who thought there was little difference between Carter and Ford, but might hesitate to cast a third-party vote if that would help a more conservative Republican than Ford...
(3) What about the South? First of all, remember that Reagan did not win
all the southern primaries: Ford defeated him in FL, TN, and KY. Second, Carter, as the first major-party presidential candidate from the Deep South since before the ACW, generally won decisive, not narrow victories over Ford in the South. He lost VA and OK (and I assume he would have done so against Reagan as well) but the only southern states he carried by less than 5.78 points were MS and TX.
https://en.wikipedia.org/wiki/United_States_presidential_election,_1976 Note that if Reagan carries both TX and MS but loses OR, he will still fall short of 270 electoral votes.
But might Reagan have carried some southern states Carter won
decisively in OTL? I doubt that. One piece of evidence of Carter's appeal in the South against Reagan is that
even in 1980 when Carter had of course become a very unpopular president, he came very close to beating Reagan in southern state after southern state: Reagan won TN, AR, AL, MS, KY, and SC by 1.53 percent or less, and NC by 2.12 points. He did win LA by 5.45 points but by then Carter's energy policies were very unpopular there. (And of course he won FL by a landslide but the Mariel boatlift crisis and the unpopularity of Carter's Middle East policy among Jewish voters doomed Carter in that state in 1980.) Indeed, it is ironic that although the South was Anderson's weakest section in 1980, it is the section where he might have cost Carter a few states...
(4) In the Northeast and Midwest, I cannot see Reagan carrying any state that Ford didn't win, and indeed he might have lost some major states that Ford won narrowly in OTL--Illinois (where Ford easily defeated Reagan in the primary) and NJ. And just maybe even MI--yes, Carter lost it by over five points in OTL, but after all it was Ford's home state.
So
could Reagan have defeated Carter in 1976? Sure--in a close race, anything is possible.
Would he have done so? I doubt it.