Why is the line from Seth to Noah often called righteous?

This is related to alternate interpretation of Genesis 6:4

There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.

The traditional interpretation until relative modernity was that which is found in the apocryphal book of Enoch, which church fathers like Tertullian used in explaining this passage. That explanation is that "sons of God" means "angels" and "daughters of men" means "human women." So angels came down and slept with women.

Entering into modernity, this explanation was seen as unacceptable, and so an alternative was needed. Hence the "sons of God" now becomes the line of Seth, and the "daughters of men" becomes the line of Cain. And viola, the "mythological" interpretation is gotten rid of.

Is there any evidence in the Bible to say that the rest of Seth's ancestors were righteous rather than just being sinful like everyone else?

Potential Answer: Embedded at the end of both the genealogies are poetic references to what appear to be a pre-Noahetic bronze age. One ancestor Lamech from the Cain side brags to his wives that he can use this new found technology that his son has developed to fashion weapons and kill young men; the other Lamech on the Seth side looks as though he is thankful that this new technology can be used to fashion tools to farm with:

Cain Side:

Gen 4: 22 Zillah... also gave birth to Tubal-cain, the forger of all implements of bronze and iron... Lamech said to his wives, “Adah and Zillah, Listen to my voice, You wives of Lamech,Give heed to my speech, For I have killed a man for wounding me; And a boy for striking me; 24 If Cain is avenged sevenfold, Then Lamech seventy-sevenfold.”

Seth Side:

Gen 5:28 Lamech lived one hundred and eighty-two years, and became the father of a son. 29 Now he called his name Noah, saying, “This one will give us rest from our work and from the toil of our hands arising from the ground which the Lord has cursed.”

The embedded poem and phrase in the genealogies underscores the differences between them, one side using this power for food, the other to kill. One remains somewhat God centric in thought abet negatively the other indicative of self centric hard hearted boasting over death.

What could have triggered the flood was the intermarrying between these two morally divergent genealogical lines.

Son's of God taking the daughter's of men There is a defense for the "sons of God" being Cain side human rulers of the time, they intermarried with the Seth side and so destroyed that side's morality, plunging all humanity into a degraded state that precipitated the great flood. See Bruce Waltke's Commentary on Genesis for more information on this.

Methuselah As far as Noah's ancestor is concerned, maybe not affected by the intermarriage morally. His death possibly prophetically releases the flood. (going from memory) I think inbedded in his name is the idea that judgement will not come as long as he was living; he lived longer than any other pre -flood individual, suggesting a similar mercy at work today i.e. patience of God at work postponing a second judgement.

shorthand answer: The moral diversity of the lines of Cain and Seth seems present imbedded within the genealogies themselves, the extinguishing of righteousness is a result of later intermarriage culminating in judgement right after Methuselah dies, thus keeping congruent the fraze "Noah the only righteous man."

In Noah's day, the whole world was found to be wicked at such an extreme level that God decided to destroy everything. However, it was Noah who was found to be a righteous man, blameless among the people of his day.

The Lord saw that the wickedness of man was great in the earth, and that every intention of the thoughts of his heart was only evil continually. 6 And the Lord regretted that he had made man on the earth, and it grieved him to his heart. 7 So the Lord said, “I will blot out man whom I have created from the face of the land, man and animals and creeping things and birds of the heavens, for I am sorry that I have made them.” But Noah found favor in the eyes of the Lord.

9 These are the generations of Noah. Noah was a righteous man, blameless in his generation. Noah walked with God. Genesis 6:5-9 ESV

Noah's grandfather was Methuselah, whose name means "his death shall bring judgment". According to the time of his death, he died the year of the flood--supposedly not from drowning but from natural causes. His death brought judgment.

Noah's great grandfather--and Methuselah's father--was Enoch, who is noted as having "walked with God". His walk with God was apparently so close that God took Him straight to heaven.

When Enoch had lived 65 years, he fathered Methuselah. 22 Enoch walked with God after he fathered Methuselah 300 years and had other sons and daughters. 23 Thus all the days of Enoch were 365 years. 24 Enoch walked with God, and he was not, for God took him. Genesis 5:21-24 ESV

So, we know that Enoch was a very righteous man. We also know that Noah was a very righteous man. Thus, it seems that this was a righteous lineage, where the righteous fathers passed on to their children a deep reverence for God.

The evidence is not overwhelming, to be sure. In fact, it's largely circumstantial. Still, the conclusion is reasonable.

I don't think anyone argues that all of Seth's line was blameless. The argument is that Seth's line had special favor from God, Cain's line did not, and that the rebellion of Seth's line was (or was caused by) intermarriage with Cain's offspring.

Matthew Henry comments on the circumstances leading to the Flood:

In all ages there has been a peculiar curse of God upon marriages between professors of true religion and its avowed enemies. The evil example of the ungodly party corrupts or greatly hurts the other. Family religion is put an end to, and the children are trained up according to the worldly maxims of that parent who is without the fear of God. If we profess to be the sons and daughters of the Lord Almighty, we must not marry without his consent.

Earlier, he comments on the births of Seth and Enosh:

Our first parents were comforted in their affliction by the birth of a son, whom they called Seth, that is, 'set,' 'settled,' or 'placed;' in his seed mankind should continue to the end of time, and from him the Messiah should descend. While Cain, the head of the apostacy, is made a wanderer, Seth, from whom the true church was to come, is one fixed. In Christ and his church is the only true settlement. Seth walked in the steps of his martyred brother Abel; he was a partaker of like precious faith in the righteousness of our God and Saviour Jesus Christ, and so became a fresh witness of the grace and influence of God the Holy Spirit. God gave Adam and Eve to see the revival of religion in their family. The worshippers of God began to do more in religion; some, by an open profession of true religion, protested against the wickedness of the world around. The worse others are, the better we should be, and the more zealous. Then began the distinction between professors and profane, which has been kept up ever since, and will be, while the world stands.

Though we don't learn too much about most of Cain's line or Seth's, some significant things are mentioned about the three generations of Seth's line just before Noah. Enoch "walked with God" and was taken away. His son Methuselah was the longest-lived man ever; longevity is strongly associated with blessing. His son Lamech prophesied that Noah would bring "rest," indicating that he was weary of the sin around (and perhaps within) him.

In 2 Samuel 7:14 God says David will be his "son." In the New Testament, the elect are often called "sons" or "children" of God. In the Old Testament, it's well-known that the elect line was through Abraham, then through Isaac. Those who say Seth's line was "righteous" would say that it's not a stretch to consider that line to have begun with Seth.

To drive the point home, the sin of God's people (or his "children") intermarrying with pagans is a huge theme in the Old Testament after the flood. Over and over Israel is punished for marrying Canaanites or chastised for taking Egyptian or Edomite or Moabite wives. Over and over Israelites' unbelieving spouses tempt them to the sin of idolatry. In the New Testament Paul pleads with the Corinthians not to be "unequally yoked." Is it really a stretch to believe that it would also be a grievous sin before the flood?