If the Spirit or scripture instruct us to be clothed in public why didn't the Spirit or scripture instruct Adam and Eve to be clothed in public in God's most holy presence?
The scripture tells us that it is the Lord God who created them naked (That is, God as the three persons in one Godhead -- Gen 1: 26) The Spirit, the Son together with the Father created them naked and saw everything created as good including their nakedness, therefore, there was no reason for the Spirit to give a counter instruction! ---- unless you do not believe in the Trinity.
I do not think we can construe the garden of Eden as a public place if the only people dwelling there were just Adam and his wife Eve.
But let us analyze that scripture a little bit since I do not have idea why you asked the question?
1. The scripture says, unto the pure, all things are pure but unto them that are defiled and unbelieving is nothing pure, but even their mind and conscience is defiled (Titus 1:15). Adam and Eve were created pure, therefore, in their purity they saw everything God created as good just as God made them including their nakedness. On another note, when God asked Jeremiah, what do you see? and, Jeremiah answered. God told him he has well seen, meaning that Jeremiah saw things the way intended and purposed by God (Jeremiah 1:11-12).
What do we see when we look around us? is the question.
We see with our eyes but perceive with the heart. When the heart is defiled, the testimonies of the physical senses become false because they now see the finite rather than the eternal but the scripture enjoins us to see beyond the temporal into the eternal creation of God in order to see his eternal goodness. So, when Adam and Eve's mind and conscience were defiled by sin, they saw evil in what was hitherto good because what they saw was the defiled body, hence, their shame. They could no longer see the eternal goodness of God. Man's perception is usually clouded by sin.
2. The narration of the fall of man in Genesis in my opinion, shows that Eve had already sinned in her heart before even eating the fruit of the tree of the knowledge of good and evil. We can deduce this from her discussion with Satan. The scripture tells us that she saw the tree as capable of making one wise. (likely outcome from the discussion) But, we know this is not a feature of the tree, for God did not say so. (Wisdom does not come from the creature but from the Creator, from God himself). This means that she imagined it and perceived in her heart, having swallowed hook and sinker the lies of the devil. Pride has already aroused, heightened, and there was no going back. Eating the fruit was an outward expression of that sin and a physical witness to her disobedience of the word of God.
3. The bible says she also gave to her husband who was with her and he ate. One would expect that since God singled out that particular tree and showed it to Adam, unlike the tree of Life in the midst of the garden, Adam would have known that, the fruit offered him by Eve was the forbidden fruit. What would have made him eat it ? Well, I have heard people say, it is the love of his wife that could have made him do it. I disagree, for the fact that love does not consent to evil/sin . It disapproves it, rebukes it and corrects it.
4. Eating the fruit of the tree is an outward witness of their disobedience which also places the burden of accountability on them. They now know what is good and evil and should now account for their actions and be responsible for them. Even today, in our own dispensation this responsibility stands.
5. I personally think there is nothing wrong in being naked. There are still tribes in remote villages in the world that do not wear clothes and they see that as normal. However, in public which is what your post is addressing, there is a guiding principle for Christians. Paul tells us in 1 Corinthians 10:23 that all things are lawful for us but not all things are expedient; all things are lawful for us but not all things edify.
He tells us further in 1 Corinthians 8: 9 - 13, to take heed lest by any means our liberty become a stumbling block to them that are weak. For, if any man sees you who has knowledge do this, the conscience of him which is weak be emboldened to do the same, and through your knowledge shall the weak brother perish for whom Christ died? But, when you sin so against the brethren and wound their weak conscience, you sin against Christ. So, if this thing makes my brother sin, I will refrain from it while the world stands lest I make my brother to offend.
We must sacrifice our liberty for the benefit of our weak brothers and sisters.
You can now judge for yourself, if as a Christian, wearing cloth in public is good or bad.