Has no one heard Billy's version? I believe it was written by someone else, with the author, or Billy, adding the Grateful Dead line?
And maybe it has no connection to Daniel Prayed, other than the similar sound?
OK, after a few weeks of no response, I went to the higher power. No, not JESUS, but Google AI! I've only been using it for a week and I can't believe the smart, logical answers it gives. I've been asking odd questions, like above, to see what it knows. And so far, I'm lovin' it!
...

The primary similarity between "Daniel Prayed" and "If Your Hair's Too Long" is that they are both American folk or bluegrass gospel songs that draw upon biblical or religious themes to deliver a moral message.

While they come from different eras and have different tones, they share several core characteristics:

Biblical/Gospel Foundation: Both songs are rooted in the tradition of Christian gospel music. "Daniel Prayed" is a straightforward retelling of the Old Testament story of Daniel in the lions' den, highlighting themes of faith and perseverance. "If Your Hair's Too Long" is a satirical take on a specific, legalistic interpretation of Christian doctrine, using the biblical story of the rich young ruler to mock a rigid moral code.

Moralistic Messaging: Both songs convey a moral or spiritual message. "Daniel Prayed" is a serious and uplifting hymn that encourages listeners to be faithful in their prayers and trust in God's deliverance. "If Your Hair's Too Long" uses humor and exaggeration to criticize a superficial understanding of faith, suggesting that judging others by their appearance (like hair length) is a distraction from a true spiritual life.

Genre and Style: Both songs are firmly in the vein of traditional American folk and bluegrass music. They are often performed with acoustic instruments like guitar, banjo, and fiddle, and feature vocal harmonies typical of gospel quartets or old-time music.

In essence, they are two sides of the same coin: one is a devout and serious expression of faith, while the other is a tongue-in-cheek critique of a certain kind of religious rigidity, but both songs speak to the deep and often complex relationship between faith, tradition, and personal conduct within American culture.

So, there - question answered. Enough to my satisfaction. I'd have to hear from the writer of 'hair' go get a more informed answer, but I'm fine with what AI gave me.