They shall join you and keep guard over the tent of meeting for all the service of the tent, and no outsider shall come near you.
Numbers 18:4

A gentile can be a sojourner in Israel, a citizen in all but inheritance in the land, and eventually be adopted into one of the tribes and inherit land along with the native born. But a gentile convert can never become a Levite, let alone a Levitical priest. God's covenant with Aaron is open only to the physical descendants of Aaron. Anyone trying to usurp that priestly role at the altar or any of the other holy articles of the Tabernacle or Temple was to be killed.