score:5
"Matthaean priority" comes in two primary forms: the Augustinian hypothesis and the two-gospel hypothesis. Both hold that Matthew came first, but differ on which synoptic gospel came next (Mark in the Augustinian hypothesis; Luke in the two-gospel). They are minority views in NT scholarship, but some respected scholars have argued for them in recent years. Among them are:
In previous generations, scholars like Johann Jakob Griesbach, John Chapman, Christopher Butler, and William Farmer held similar views. Of course, so did many in the early church, but that's another story.
As for the relative popularity of these views as compared to Marcan priority, Christopher Tuckett's article "The Current State of the Synoptic Problem" (2008) may shed some light. He describes the dominant solution to the Synoptic problem (the two-source hypothesis, which defends Marcan priority) and identifies several trends:
That said, many believers in the inspiration and inerrancy of scripture (B. B. Warfield, Geerhardus Vos, A. T. Robertson, etc.) have supported the two-source hypothesis, so there isn't a clear dividing line on this issue between defenders of historicity and those opposed to it.
All told, we can safely conclude that Marcan priority is clearly dominant β Tuckett tells us that two of the top three schemes for solving the Synoptic problem rely on it. But moreso today than 40β50 years ago, scholars acknowledge weaknesses in the dominant theories, and are generally less inclined to dismiss Matthaean priority out of hand.