This scripture does not say that excrement is unholy. It says the camp must be holy; and that defecating in the camp would be indecent. Not to mention unsanitary and unhealthy.
When Isreal left Egypt, Exodus 12:37 states that there were 600,000 "men of foot." Men of foot is generally considered men of fighting age. The modern US military considers men of fighting age to be between 16 and 49. So, this does not include women, children, or the elderly. It is estimated that over 2 million people left Egpyt.
For 40 years the Israelites wandered in the wilderness (Numbers 32:13). 2 million people living in tents for 40 years in the desert can be dangerous. A simple cold could wipe out most of the nation. This is why God gave Isreal many commandments that were less about righteousness and more about maintaining a health camp. Like not defecating in the camp.
Leviticus 5:2, 3; Numbers 19:16. Laws about touching dead bodies.
Leviticus 14:8-9. Isolating the sick outside the camp.
Leviticus 15:4-27. Laws required bathing and clothes washing.
Deuteronomy chapters 12, 13, 14, 23 and many more.
God is not calling excrement unholy He is saying that defecating in the camp would be unholy, unclean, unsanitary, unhealthy. Even dogs know not to poop and eat in the same place.
---- Response to Comment ----
This is the exact verse I was referring to. Here the Lord is talking about how the camp should be, "therefore your camp must be holy;" This is not God suggesting excrement is unholy because of Adam. Israelites are craping in the camp! God is telling them it is indecent.
If we went camping, and my son was too lazy to walk out of camp and chose to crapped just outside our tent. I would make him clean it up and teach him exactly what God was teaching Israel...
Verse 12) You will go to a place outside of the camp
Verse 13) You will take a shovel and dig a hole, and after done, you will bury it.
Verse 14) I walk in this camp. I am here to keep you safe; therefore, you will keep this camp clean, just like you should keep yourself clean, both physically and spiritually.
According to Gesenius' Hebrew-Chaldee Lexicon, the etymology of קָדוֹשׁ is "pure, clean, holy, sacred." The root word for "holy" is clean. It would not be improper in this instance to translate "holy" as "clean."
This verse has nothing to do with Adam's sins. Nor is it about the unholiness of excrement. This is another example of the indecency and unclean behavior of Isreal.