This passage is indeed the first instance of a whole household being shown preparing for a sacrifice (though the lone pair of Abraham and Isaac were shown preparing for the sacrifice of Isaac at Gen 22:6-9). A good place to begin understanding what is going on here is simply to ask why all the family is being included; why did Jacob not simply prepare himself?
Some background will help with the answer. The Lord is often concerned with the observance of the entire family, because it is the family that passes on traditions. While none of the patriarchs' clans have yet been shown preparing for sacrifices (again, the unusual sacrifice of Isaac excepted) at least a couple other collective actions have been shown before this, in response to the Lord’s command: there was, of course, the movement of Abram, Sarai, and his family to Canaan (Gen 12:1-6); the circumcision of all the men of the camp (17:23); and the organized movement from Haran (31:20-21).
But the present verses are the first place in the Bible text in which the whole family is made holy for a group sacrifice. This is a remarkable thing, prefiguring the group preparations and anointings found in Exodus, such as Moses sprinkling blood on the people (Ex 24:8). But Jacob was the first patriarch recorded as practicing ritual purification, which is what is suggested here. The Levitical law is full of injunctions to wash and purify under this condition and that; changing garments prefigures later practices of wearing ritually purified ephods and priestly linens, and cleaning garments sullied by discharges that made them ritually impure. Jacob’s directions to his family resemble such requirements. Being rooted in law, the whole notion of being made clean for a confrontation with the Lord is thus found throughout the Bible. For example, as Matthew Henry points out, the first command in preparing for a confrontation with the Lord is to “Wash you, make you clean; put away the evil of your doings from before mine eyes” and only then, “Come now, and let us reason together” (Isa 1:16, 18). This also, as Henry aptly states, resembles baptism. The idea is quite natural: washing and changing clothes is like making oneself fresh and clean and ready for a change of heart.
But Jacob and his clan were not yet under the Mosaic ceremonial law. So we still need to address the question: why did he have them prepare at all, and why in this way? We can take a clue from Gen 35:3, in which he explains where the family is going, and why.
Interestingly, though God has commanded him in Gen 35:1, he does not tell his family so here, at 35:3; perhaps, for all they know, he has simply decided himself to do prepare the family this way. In any event, the clan, newly enlarged with Shechemite women and children (if they were not immediately sold, which is possible), is large, young, vigorous, extremely willful, and sullied by serious sin (see Gen 24). That surely is reason enough that the detailed instructions and explanation are given: there were many untaught and violent youths among them. Perhaps more importantly, Jacob is teaching his own sons the rules and substantive theological justification for performing a sacrifice. After what certainly appears to have been a disaster at Shechem, Jacob probably decided his family needed this lesson, if he was not specifically inspired by God himself to give it.
Part of the lesson concerned the offensiveness of idols. A careful examination of the text makes it clear that up to this point, the Lord has not actually forbidden the worship of other gods. The beginnings of the injunction against idolatry begins in the third generation, not the first or second. Perhaps—and I admit this is pure theological speculation on my part—the reason for the silence about idols was that the Lord wanted a robust, faithful tradition of worship of himself to have taken root before he gave the Israelites such a potentially difficult command. Abandoning a religion can be a tall order for many people, after all, and deep roots in a family tradition would help. However that might be, these verses are indeed the origin of the struggle of Israel against idolatry. So perhaps, just by the way, we need not conclude that Rachel was personally being rebuked by Jacob—but her death soon after this, in childbirth, might suggest a rebuke by God.
So, while some readers might find it startling to be told that there were any "strange [foreign] gods" (35:2) among the clan, perhaps we can understand better why they were there. But even Jacob's own wife, Rachel, “had stolen the images that were her father’s” (31:19). Moreover, as some commentators aptly point out, the brothers have just looted Shechem and captured the women and children of the city; hence it is likely that they had some idols among them. Monotheism would have had to be taught to these people, especially servants whose parents were still steeped mostly in the polytheistic pagan beliefs of the Arameans and Horites.
But let us get clear on one point. Disposing of idols, or “strange gods”, was necessary according to the later second commandment (Ex 20:4), but how did Jacob, who lived long before this revelation, know to rid himself of these idols? Partly, this seems to be a matter of common sense, given what the patriarchs had already been shown: there is only one Lord, who calls himself El Shaddai, God Almighty, the creator of Heaven and Earth, who rules in Heaven and dispatches his messengers to Earth as Jacob saw in the vision of the Ladder (28:12-15). But more to the present point, as Jacob now informs his followers, this same God “answered me in the day of my distress, and was with me in the way which I went.” (35:3) Doubtless, Jacob was remembering his own vow to the God of Beth-el: "If God will be with me, and will keep me in this way that I go... So that I come again to my father's house in peace; then shall the Lord be my God." (28:21-22) This means that, if Jacob is to keep his vow, the God to whom he will be sacrificing is his only God, his exclusive God. Preparation for this sacrifice thus would have to mean repudiating all pagan gods. It also implies that the sacrifice will be as a thanksgiving.
Thus his sons and followers (new and old) are actually being inducted into the very religion of the Lord, as Jacob has himself learned it. This requires, as Isaiah puts it, that a follower of the Lord “shall cast his idols of silver, and his idols of gold, which they made each one for himself to worship, to the moles [which live underground] and to the bats [which live in dark caves]” (Isa 2:20). Thus the idols and earrings must be buried.
But, you might say, earrings? Why dispose of them? The word translated by the KJV as “earrings” is נֶזֶם or nezem, glossed “a ring (worn as an ornament)”, but it is part of the phrase translated “earrings which were in their ears”; so earrings are definitely meant.
Such earrings seemed to have had some pagan ritual significance. There are several reasons to think so. The present text describes two sets of objects in poetic, parallel construction, “all the strange gods which were in their hand” and “all their earrings which were in their ears”, and then Jacob “hid them under the oak which was in Shechem.” This implies that the two sets of objects were alike in impurity, because they were described and treated alike. When Aaron goes to make the disastrous golden calf, he instructs the people to “Break off the golden earrings, which are in the ears of your wives, of your sons, and of your daughters, and bring them to me.” (Ex 32:2) The golden calf was made of earrings and only earrings. With sons wearing earrings, we see that they earrings were not merely female ornaments. In Judges, Gideon tells the people, “I would desire a request of you, that ye would give me every man the earrings of his prey. (For they had golden earrings, because they were Ishmaelites.)” (Judg 8:24) This further clarifies that men wore earrings as well, and that the more pagan Ishmaelite tribe were known to wear them.
But, just by the way, it is clear from a later-written proverb, “An earring of gold, and an ornament of fine gold, so is a wise reprover upon an obedient ear” (Prov 25:12), that by Solomon’s time, hundreds of years after Gideon, earrings need not have had more than an ornamental significance. See also Isa 3:20 and Ezek 16:12. I see no evidence after the book of Judges that earrings had a significance or use other than ornamental.
Finally, why bury the items used in pagan idolatry under an "oak"? “Jacob hid them”—presumably, buried them in the soil—“under the oak which was by Shechem.” (Gen 35:4) Note that the definite article is used in the word that translates “oak,” here in the form הָאֵלָ֖ה or haelah (glossed “terebinth”). The definite article might suggest this oak was previously introduced in the text, or was otherwise known to the reader. There was such an oak, previously introduced, way back when Abram first arrived in Caanan: “Abram passed through the land unto the place of Sichem [Shechem], unto the plain [i.e., “oak” or terebinth tree] of Moreh.” (12:6) This could well be the intended to be the same tree: it might have been a famous "oak" with significant meaning for the family going back to the days of Abram. If so (and this is all rather speculative), then perhaps the notion is that these pagan items would be rendered harmless by their presence in "holy ground."
But of course it is also possible that they were buried under a random tree where they would never be found again.