Esau and Edom:
It's all too easy for us all to simply label our enemies with the broad stroke of "Edomites" (Esau), but is this actually biblical?

We'll look at the history of Edom, and it's founder Esau, starting at Genesis 25-32:
—Esau and Jacob are twin brothers. Sons of Rebecca and Isaac, son of Abraham.
—Isaac loved Esau and wanted to give him the birthright.
—Jacob tricked Esau into giving him the birthright.
—Jacob tricked Isaac into giving him his blessing.
—Esau vowed to kill Jacob for his deceit.
—Esau betrayed his family also, marrying forbidden local Canaanites.
—Their descendants were still Adamic, demonstrated by their allowance to assimilate [Deu 23:7-8].
—Brothers meet again years later, Esau commands huge armies which Jacob feared for the lives of his people.
—Esau however did not attack, ran to Jacob and hugged him (Reconciliation of Jacob and Esau), despite everything, they were still brothers.
—Their descendants however continued to be extremely hostile to each other [Psa 137:7], the Edomites even aiding the sacking of Judah.
—"Jacob I loved, but Esau I hated" [Mal 1:2-3] is often falsely quoted to drive the narrative they were some demonic alien tribe, but when quoted by St Paul [Rom 9:13-14] it is abundantly clear this was loaded language to add emphasis, all it meant was "Jacob I chose, but Esau I rejected".
—Edom's destruction is prophesied [Oba 1] and would shortly occur, despite the continued use of the name against future unrelated rivals such as Judaeans against Rome, Rome against Muslims, England and France against each other, etc.

According to "The Religion of Idumea and Its Relationship to Early Judaism" (Levin, 2020) after the collapse of the Kingdom of Edom, they were ethnically replaced by Arabs who adopted an Edomite identity under the name "Idumaean".

Summary of the transition from Edom to Idumaea (Levin, 2020):
—Kingdom of Judah falls in 586ᴮᶜ.
—Kingdom of Edom covered either side of Arabah Valley and the Negev Desert.
—Edom abolished in 552ᴮᶜ by Neo-Babylonian King Nabunidus, eastern territory overrun by Qedarite and Nabatean Arabs (mixed).
—Arabs assist Persian King Cambyses conquer Egypt and Edom's western territory in 525ᴮᶜ, as reward, Edom's former territory and Gaza trade routes are granted to Qedarite Arabs [Herodotus Histories 3:4-9].
—Alexander the Great razed Gaza in 332ᴮᶜ, ending Qedarite rule of the region and trade routes, started by Cambyses.
—An administrative body known as Idumaea emerged (Greek name, inspired by new Greek influence), encompassing the regions southwest of the Dead Sea, with some reach in the southern Judaean hills, and Negev Desert.
—Hasmonean ruler John Hyrcanus I absorbs Idumaea into Judaea in 107ᴮᶜ (Antiquities 13:256-257; Wars 1:63).

Further analysis (Levin, 2020):
—The epigraphic record on Idumaean citizen name origin infers an Idumaean demographic that is: 30% Arab, 30% West Semitic, 25% Edomite, 10% Judahite, and rest Aramaic, Egyptian and Phoenician.
—In the north of Idumaea (Arad), the demographic is: 61% Judahite, 14% Edomite, 12% Arab.
—Strabo Geographica 16:2.34 claims Idumaeans were originally Nabatean Arabs.
—(Reich, 2011) Modern Jews attained their negro admixture 72 gens ago (~2200 years, 30/gen) while Druze attained this 44 gens ago (~1300 years, 30/gen).

In Summary: after the fall of Judah and Edom. Edom was erased as a nation and ethnically replaced by Arabs.

The surviving Edomites settled in a region that would later be known as Idumaea; however they quickly became a small minority even in that land, so much so that Greek historians (Strabo) would mistake the Arab majority as being the Edomites. Perhaps Hyrcanus mistook them as well when absorbing Idumaea.

Idumaea became an ethnically blurred melting pot of: Arab (mainly), Edomite, Judahite, and Phoenician; which would all identify as "Idumaean".

Modern Jews attained their negro admixture at this time (~200ᴮᶜ) which other Levantine peoples didn't attain until (~ᴬᴰ700) during the Arabic expansion, demonstrating Jews weren't Judahites nor Edomites, but mixed Qedarite Arabs.