It is actually Jewish law that a priest has to serve barefoot. The source is in the Talmud, Tractate Zevachim 24a
This is derived as the Sage from the school of Rabbi Yishmael taught:
Since the floor of the Temple courtyard sanctifies the priest to
perform the service, and service vessels, i.e., priestly vestments,
also sanctify him, one may draw a comparison between the two: Just as
with regard to service vessels, nothing may interpose between the
priest and the service vessel, so too with regard to the floor,
nothing may interpose between the priest and the floor.
This is codified in law codes, e.g., Rambam's Mishne Torah (Biat Hamikdash 5:17)
Anyone involved with one of the Temple services must be standing on the floor. If there was anything intervening between himself and the
ground, e.g., he was standing on a utensil, an animal, or a
colleague's foot, [his service] is invalid.