Did a brief search of the forum and couldn't find a recent discussion on this.
Suppose Mary is born Martin, and James V dies as OTL. There's still a long regency in store for Scotland (we'll presume Martin doesn't inconveniently die in infancy or early childhood) but the King would naturally remain in the country during his minority, potentially at risk of being a focus of intrigue.
Would the Scottish regency be in a hurry to make a French match for King Martin, as they were with Mary, if there is even a suitable girl available?
Further, how does it affect Henry VIII's marriage politics that Scotland's King is a viable potential claimant to the English crown? The reluctance of England to accept a ruling Queen would work against Tudor succession, and potentially mean King Martin is favored in some quarters. If Martin remains Catholic while Henry breaks with Rome, that's even more of a risk.