In regards to "Why do even non-Christians look down on men with long hair?", your quote associating long hair with a rebellious attitude is only a post 60's statement, only. I don't know of another time when long hair was a sign of 'rebellion' outside of the era of the 60's.
Many of the European American forefathers had longer hair that they were able to pull back as well as the white wigs. Many Nordic, Celtic, Germanic ethnic groups, the men had long hair. It's assumed in our times, but that doesn't mean a whole lot of time is spent tending to it. It depends on the hair texture.
I will disagree with this though, because we tend to look at history through the eyes of the present. Many civil societies of past and present had the majority of men with long hair, and it had no projection of them making a statement. Even though in particular cases that is true. But it doesn't have to be bad. I believe it was the prophet Isaiah or Ezekiel that God told to shave himself (as well as lay naked in the street) to make a statement of prophecy to Israel of coming judgment. Many native American men and braves or warriors wore their hair long. Blacks Americans during the 60's & 70's started wearing afro as a sign of appreciation of their natural hair. Many prior to that were made to feel ashamed and either kept it cut short or processed it to try to fit in with the dominate 'white' society.
Also the Nazarite vow required that a man do not cut his hair. Samson as active as he was never had a razor to his hair. Short hair was something a bit more common during Paul's time, because the 'caesar' cut was popular starting in Rome, Italy. But prior to that many Hebrew men wore their (bushy curly) hair at least to the neck.
In the referenced answer, I already addressed the fact that Paul stated on multiple occasions, including the letter to Corinth, that he was writing on behalf of God and was not asserting his own opinion. Even when he was discussing divorce he stated, "Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband" (I Corinthians 7:10). Paul wanted people to know that he is not the only one stating the command; he is making it clear that this was something Jesus taught while on earth (Matthew 19:1-10). But Paul also addressed issues that Jesus didn't discuss while on earth. "But to the rest I, not the Lord, say: If any brother has a wife who does not believe, and she is willing to live with him, let him not divorce her" (I Corinthians 7:12). The fact that Jesus didn't discuss it while on earth doesn't make Paul's command any less authoritative. A bit later, Paul raises the challenge, "If anyone thinks himself to be a prophet or spiritual, let him acknowledge that the things which I write to you are the commandments of the Lord" (I Corinthians 14:37). To lightly dismiss something that Paul wrote as "only his opinion" or "only stating what was cultural in his day" is to place yourself in opposition to God.
The topic of hair length is actually a supporting argument to discussing whether women ought to wear a head covering while praying and prophesying. I won't repeat that has been said about those matters, but you can read them in the Question and Answer section under the topic of Head Coverings. But one point needs to be reemphasized. Paul based his arguments not on current fashion but on things that have always been true. He based it on the role of men and women from Genesis 3. He based it on the order of creation from Genesis 2. He based it on nature -- that it takes both men and women to produce men and women. Finally, he appealed to what was naturally apparent: "Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering" (I Corinthians 11:14-15). His argument is based on natural tendency and not immediate cultural practices. In fact, the commentator Adam Clarke argues that in that region it appears men tended to have long hair. "Nature certainly teaches us, by bestowing it, that it is proper for women to have long hair; and it is not so with men. The hair of the male rarely grows like that of a female, unless art is used, and even then it bears but a scanty proportion to the former. Hence it is truly womanish to have long hair, and it is a shame to the man who affects it. In ancient times the people of Achaia, the province in which Corinth stood, and the Greeks in general, were noted for their long hair; and hence called by Homer, in a great variety of places, karhkomowntev acaioi, the long-haired Greeks, or Achaeans. Soldiers, in different countries, have been distinguished for their long hair; but whether this can be said to their praise or blame, or whether Homer uses it always as a term of respect, when he applies it to the Greeks, I shall not wait here to inquire." In case it is not clear, what Adam Clarke is referring to is the fact that men have a tendency to go bald and women do not.
Rebellion expressed in hair length did precede the 1960's. "At certain historical moment, such as the 1920s, short (or "cropped") hair on women was considered a statement of rebellion against established gender roles." [History of 20th Century Fashion: Understanding the History of Hair] There is an extended article, published in the Journal of American History, September 2004, titled "Flaunting the Freak Flag: Karr vs Schmidt and the Great Hair Debate in American High Schools (1965 to 1975)," that discusses the ties of long hair and rebellion.
The lack of long hair was considered humiliating for women. In warning about the coming captivity, Isaiah said, "And so it shall be: instead of a sweet smell there will be a stench; instead of a sash, a rope; instead of well-set hair, baldness; instead of a rich robe, a girding of sackcloth; and branding instead of beauty" (Isaiah 3:24).
Yes, those under the Nazarite vow in the Old Testament did not cut their hair while the vow was in effect. The point you missed is that Samson was an exception and not a rule. Most people only took the vow for a short period of time. The vow began by shaving one's head. "All the days of the vow of his separation no razor shall come upon his head; until the days are fulfilled for which he separated himself to the LORD, he shall be holy. Then he shall let the locks of the hair of his head grow" (Numbers 6:5). If something caused him to break the terms of the vow, he had to start over. "And if anyone dies very suddenly beside him, and he defiles his consecrated head, then he shall shave his head on the day of his cleansing; on the seventh day he shall shave it" (Numbers 6:9). At the end of the vow, the hair grown while under the vow was shaved again and offered to God. "Then the Nazirite shall shave his consecrated head at the door of the tabernacle of meeting, and shall take the hair from his consecrated head and put it on the fire which is under the sacrifice of the peace offering" (Numbers 6:18). Therefore, the existence of the Nazarite vow did not imply that most had long hair. Nor does this imply that most of the Israelite population was under a Nazarite vow. Samson was a rare individual who was placed under a Nazarite vow by God prior to birth and was required to remain under it for his lifetime.
In fact, we have a hint of what was considered proper attire for hair in the rules God laid down for the priests returning from captivity. "They shall neither shave their heads nor let their hair grow long; but they shall keep their hair well trimmed" (Ezekiel 44:20).