The Jewish Encyclopedia makes this surprising factual claim:
In ancient Israel one was not required to be specially consecrated in order to perform the sacrificial functions; any one might approach the altar and offer sacrifices. Thus Gideon, of the tribe of Manasseh (Judges vi. 26 et seq.), and the Danite Manoah (ib. xiii. 16, 19) sacrificed in person at the express command of God and the angel of God respectively...
One might think these were exceptional cases, while ordinary priests operated at the Tabernacle. However, when I looked up the word "priest" in the Book of Judges, I found that although the term is used about a dozen times, none of these refers to an authorized priest at the Tabernacle. In fact all of the instances refer to a renegade priesthood, first under the wealthy Ephraimite Michah (Judges 17) and then under the tribe of Dan (Judges 18).
Other than this I find no references to priests as such in the Book of Judges. Later, Samuel acted as priest, judge and prophet. Do we know of any specific Aaronic priests in the Book of Judges itself? I see that Judges 21:19 mentions the Tabernacle being located at Shiloh, north of Bethel, but no such priests are named. Critical scholars sometimes give the opinion that the priesthood of Aaron and his descendants is anachronistic. This hypothesis is strengthened by absence of Aaronic priests in the Book of Judges.
I would appreciate additional information about the priestly office in the time of the judges.