The use of skins was deemed okay because God Himself first made coverings for Adam and Eve out of an animal skin.
However the sacrifices were burnt offerings and they were consumed by the fire. Nowhere in the sacrifice rituals did anyone ever eat the animal after it was made a burnt offering to God.
Permission was given only after the flood, after the entire earth’s ecosystme had drastically changed. And at this time God put fear of man into animals because of this change, so that they wouldn’t be hunted to extinction.
This is, at best, speculation.
Quickly following on the heels of the Fall was a time when men stopped caring about the Lord. To assume that people remained faithful to a command to be vegetarian is naive.