Another possibility is that there were factions among the Edomites with mixed feelings about the Israelites. Lands are not always united, Israel after Solomon for example. Also note that Edom is used in the first citation and Esau in the second. Esau was blood; his wives were not and people of the land. Both sides had reason to suspect Israelite intentions. Esau is only Edom in reference to the red pottage used by Jacob to buy his birthright and by the rose red rock and hairlike striations (Esau was red and hairy.) of Edom. In one sense it is a condescending name, in the other descriptive. Esau and Jacob made up with each other in Genesis, but his pagan wives and Ishmaelite wives would likely be more inclined to hold grudges by their circumstances. Isaac liked Esau. Jacob wronged him for all that, though the Jews including the author of Hebrews try to make Esau the offending party, rather than the supplanter, Jacob. So one faction could have prevented crossing, and another faction in a different area allowed it, we suppose by reason of both fear and financial gain. And the demise of the Edomites was likely more against the feminine side of the land than Esau. But the captain of the ship takes the blame. The Edomites had their faults; the Israelites certainly had theirs, described as worse than the Canaanites by God at one point. If God loved Jacob and hated Esau, Israel was a thorn and distress to God, returning evil for good. If God is love, is not his hate motivated by love? You would suppose so.
Response to Speculation and Citation Complaint:
Division of Kingdoms:
1 Kg 11:31 And he said to Jeroboam, Take thee ten pieces: for thus saith the Lord, the God of Israel, Behold, I will rend the kingdom out of the hand of Solomon, and will give ten tribes to thee:
Origin of Edom Name:
Wikipedia: Edom The Hebrew word Edom means "red", and is derived from the name of its original founder, whose name was Esau, the elder son of the Hebrew patriarch Isaac, because he was born "red all over". (Gen 25:25 )Later, as a young adult, he ate "red pottage".(Gen 25:30) The Tanakh and the New Testament both describe the Edomites as descendants of Esau.
Esau and Jacob Reconciled:
Gen 33:1,3-4 And Jacob lifted up his eyes, and looked, and, behold, Esau came, and with him four hundred men. And he divided the children unto Leah, and unto Rachel, and unto the two handmaids. .... 3 And he passed over before them, and bowed himself to the ground seven times, until he came near to his brother. 4 And Esau ran to meet him, and embraced him, and fell on his neck, and kissed him: and they wept.
The Wrong to Esau:
Gen 25:30-32 And Esau said to Jacob, Feed me, I pray thee, with that same red pottage; for I am faint: therefore was his name called Edom. 31 And Jacob said, Sell me this day thy birthright. 32 And Esau said, Behold, I am at the point to die: and what profit shall this birthright do to me?
Esau in Conformance with Prudent Man:
Matt 5:40 And if any man will sue thee at the law, and take away thy coat, let him have thy cloak also.
Matt 6:34 Take therefore no thought for the morrow: for the morrow shall take thought for the things of itself. Sufficient unto the day is the evil thereof.
Gen 26:34 And Esau was forty years old when he took to wife Judith the daughter of Beeri the Hittite, and Bashemath the daughter of Elon the Hittite:
NOTE: Waited till forty for women. Married them and not consorting with prostitutes.
Heb 12:16 Lest there be any fornicator, or profane person, as Esau, who for one morsel of meat sold his birthright.
NOTE: Esau sold his birthright under duress. Jacob, his brother, shook him down out of greed. Hebrews is an epistle. The writer's opinions are his. It is scripture that he said it, that is all. Note the citation is not an oracle from God. It is nonsense to suppose opinions of Paul, Barnabas or any apostle is divine unless specifically stated.
Iniquity of Jews:
2 Chr. 33:9 So Manasseh made Judah and the inhabitants of Jerusalem to err, and to do worse than the heathen, whom the Lord had destroyed before the children of Israel.
Malachi 1:2-3 I have loved you, saith the Lord. Yet ye say, Wherein hast thou loved us? Was not Esau Jacob's brother? saith the Lord: yet I loved Jacob, 3 And I hated Esau, and laid his mountains and his heritage waste for the dragons of the wilderness.
Rom 9:11-15 (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth;) 12 It was said unto her, The elder shall serve the younger. 13 As it is written, Jacob have I loved, but Esau have I hated. 14 What shall we say then? Is there unrighteousness with God? God forbid. 15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
NOTE: We see mercy not righteousness of Jacob at work here. If God is good, we must suppose some good intent in an otherwise arbitrary decision. Neither Jacob nor the Jews were righteous.