The question is, "Why were Saul and the prophets not ashamed when nudity was a source of shame to Adam and Eve?" – Faulty Question! It's 100% wrong to say, "nudity was a source of shame to Adam and Eve." The Bible says explicitly that God made them naked, it was good, and they were not ashamed
-- it was sin that made them ashamed, NOT nudity! Most Western cultures get this backward.
Nudity in the Gospels
The innocence is further clarified in the Gospel of Mark and in Hebrews: Jesus was the second Adam. Adam brought shame with his sin. Jesus set us free from the shame of sin. When the soldiers arrested Jesus, they seized a young man, but he ran away naked and free. (Mark 14:51-52) It is CLOTHING that "represents" sin and shame. If you feel shame when nude, you are in bondage.
Nudity in the Prophets
God tells no one to sin, and He told Isaiah to go naked and barefoot. (Isaiah 20:2-4, which specifies naked didn't mean still wearing underpants, as some Theologians say, because it clearly sites bare buttocks.) The prophet Micah went naked. (Micah 1:8.) Chances are, a sign of a prophet was nudity. Saul joined in because it was not exclusive to prophets. Anyone could go nude. Men in the Bible wrestled nude. (Deuteronomy 25:11) People lounged in the evening naked (Habakkuk 2:15). It's well documented that in biblical days, people in neighboring Egypt, Rome, and Greece sometimes went naked. So IF nudity were a sin, God would've most certainly and Clearly said, “Thou shalt not go naked," and He would've defined the punishment for it. (I've been taught that tithing is the only "rule" with no penalty. So tell me the punishment IF nudity were a sin!)
Nudity in Genesis
Read Genesis carefully. Adam was already clothed with leaves when he hid in the trees and said, “I am naked.” The fact that God taught Adam and Eve to make durable clothing doesn't mean cotton, linen, and fig leaves became a sin. God was sending them out into thorns and thistles, and God knew leaves wouldn't protect them. (Animal skins are never again referred to in the Bible in the context of clothing.) It does not mean nudity (which God said was good) became a sin. Otherwise, God would not have later told some people to go nude. Jesus taught us how to pray, so do you proclaim that any prayer except the Lord's Prayer is a sin? If Jesus were to say, "Cast your nets on the left side of the boat," is it a sin to cast your line on the right side of a boat? When God let the Israelites pass through the Red Sea and later the Jordan River by walking on the ground, is it now a sin to use bridges—that we are required to use subways under the water? So how can "showed them how to make clothes from animal skins” possibly imply nudity is a sin? By the way, Adam & Eve made garments to cover their loins/hips—Eve remained topless. (Gen 3:7. - 14 of 34 sampled translations make topless clear; the remainder chose to “buffer” the original Greek to “covering.”)
If you want a rule against nudity, you don't first have to add it to the Bible. We made a law that a business can't be a monopoly, and it didn't have to be in the Bible. If your church's youth group sneaks off during summer camp and skinny-dips in the lake, you don't have to lie and say the Bible says nudity is a sin because it doesn't. You can simply say, "Our rule here at Camp Tonka-Tonka is no nudity." (IF I were a camp employee, I’d merely lecture about swimming without a lifeguard.)
Finally, we are Christians. Not Jews. We Do Not Live By The Law! We have been set free from the law. Yet some Christians invent a law and shame people into obeying. There is not to be shame anymore. In Christ there is no condemnation! (Romans 8:1.)
Don't say, 'Nudity was a source of shame to Adam and Eve,' because that absolutely is not true. Sin brought shame, and their fig leaf clothing did not take it away. Jesus took it away. And contrary to the pictures on your Sunday school wall, Jesus hung on the cross nude. That's how crucifixions were done and how Christ took away our shame.