The 1830 typesetter changed their priests to the priests. One possible explanation for the change is that the typesetter was influenced by the two occurrences of the people in the following text, especially the second occurrence of the people, which would have occurred just below in the next manuscript line of 𝓞. Both clauses have the same basic syntax and are visually similar:
their priests left their labor to impart the word of God
the people also left their labors to hear the word of God
Thus the change in the first clause of their priests to the priests could have been caused by the syntactic and visual similarity of the two clauses.
Another possibility is that the original text actually read the priests and that early on in the transmission of the text the definite article the was changed to their because of the following their labor. We have evidence for such an error tendency elsewhere in the manuscript transmission of the text:
Also see the discussion under 1 Nephi 10:3 and 3 Nephi 2:12.
Despite this error tendency, there is substantial evidence elsewhere in the text for the priests of a people to be referred to as “their priests”:
Notice, in particular, the example in Mosiah 27:5 in which their priests is followed by two instances of their (“with their own hands for their support”). Thus there is inherently nothing wrong with “their priests left their labor” in Alma 1:26, although it is always possible that the their is an error influenced by the following their labor. The critical text will here accept the earliest reading of the text since it works quite well.
We note that the text refers to the priests as having “left their labor” but the people as having “left their labors”. One wonders if the disagreement in number for labor might be an error. The plural labors for the people is probably correct since later in the verse the people are referred to as returning “unto their labors”:
On the other hand, the text can refer to the labor of the priests (that is, in the singular):
The text permits variation in referring to the labor or the labors of people, as in Alma’s statement to Korihor:
Thus the critical text will allow the variation involving labor(s) in Alma 1:26.
Summary: Restore in Alma 1:16 their priests, the reading of the printer’s manuscript (the earliest extant text here); also maintain the variation in the number for labor: “their priests left their labor … the people also left their labors”).