Does the enjoining the good and forbidding evil violate the very basic human rights of freedom to life if enjoining the good and forbidding evil compromises the dignity of someone who fails to carry out an obligatory act or perpetrates a prohibited act, and humiliates him before the people? If not, please provide reasons based on Quran/Hadith.
It's important to note here that enjoining that which is good and forbidding that which is evil is not the same as being judgemental.
Allah does not like the public mention of evil except by one who has been wronged. And ever is Allah Hearing and Knowing.
If [instead] you show [some] good or conceal it or pardon an offense - indeed, Allah is ever Pardoning and Competent.
If someone did (allegedly) do anything evil, only those who had actually been wronged by them have any real grounds to drag them through the mud for it (although it's still better to forgive in that case).
However, if I tell you that there is great blessing if you give in charity, seeking nothing but the reward of Allah rather than to be seen of men, that is enjoining that which is good. If I tell you that harming others or taking their property without just cause is bad, that is forbidding that which is evil. Whether you had done any of the evil I'm forbidding or any of the good I'm enjoining is irrelevant.
In other words, enjoining that which is good and forbidding that which is evil is predominantly a matter of preaching and there isn't necessarily any element of public shaming in it, although it may also involve acting (e.g. stopping or speaking against an evil in progress) which needs only be as public as the circumstances necessitate: Judging and punishing a wrong after the fact, be that by public shaming or other means, is entirely tangential.