"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:
- "There is widespread (but by no means universal) acceptance" of Marcan Priority (page 1)
- In the early and mid-20th century, confidence in Marcan priority was extremely high, but this has ebbed somewhat in the last 30–40 years (10)
- Of the two main rivals to the dominant two-source theory (and its Marcan priority), one of them (the two-gospel hypothesis of Griesbach) advocates Matthaean priority (4, 13)
- Prominent advocates of the two-gospel hypothesis have claimed that the dominance of the two-source theory / Marcan priority is at least partially due to theological reasons (i.e., that belief in two-source theory / Marcan priority facilitates questioning the historicity of the Jesus tradition) (15)
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 – Tuckett tells us that two of the top three schemes for solving the Synoptic problem rely on it. But moreso today than 40–50 years ago, scholars acknowledge weaknesses in the dominant theories, and are generally less inclined to dismiss Matthaean priority out of hand.