Apparently this idea that Jesus was speaking to a man under a Nazirite vow or perhaps even a priest in Luke 9:59-60 // Matthew 8:21-22 is much older than I had originally thought. In Against Marcion, Tertullian appeals to the law in Leviticus 21:1-11 and Numbers 6:6-7 saying:
For as He calls to salvation him whom He does not reject, or him whom He voluntarily invites, so does He consign to perdition him whom He rejects. When, however, He answers the man, who alleged as an excuse his father’s burial,Let the dead bury their dead, but go and preach the kingdom of God,He gave a clear confirmation to those two laws of the Creator— that in Leviticus, which concerns the sacerdotal office, and forbids the priests to be present at the funerals even of their parents.The priest,says He,shall not enter where there is any dead person; and for his father he shall not be defiled; as well as that in Numbers, which relates to the (Nazarite) vow of separation; for there he who devotes himself to God, among other things, is biddennot to come at any dead body,not even of his father, or his mother, or his brother. Now it was, I suppose, for the Nazarite and the priestly office that He intended this man whom He had been inspiring to preach the kingdom of God. Or else, if it be not so, he must be pronounced impious enough who, without the intervention of any precept of the law, commanded that burials of parents should be neglected by their sons. When, indeed, in the third case before us, (Christ) forbids the manto look backwho wanted firstto bid his family farewell,He only follows out the rule of the Creator. For this (retrospection) He had been against their making, whom He had rescued out of Sodom.1
While I’d argue that Jesus recognized the man as being under a Nazirite vow (such is noticeable on appearance alone), Tertullian is saying that Christ must have intended this man either for the priestly office or Nazirite vow. But notice his conclusion if this isn’t the case: “he must be pronounced impious enough who, without the intervention of any precept of the law, commanded that burials of parents should be neglected by their sons.” Well said!
1 Tertullian, Against Marcion 4.23. Available in ANF 3.386-387 or online here.