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.
Narrated Abdullah ibn Abbas:
A man was injured during the lifetime of the Messenger of Allah (saws); he then had a sexual dream, and he was advised to wash and he washed himself. Consequently he died. When this was reported to the Messenger of Allah (saws) he said: They killed him; may Allah kill them! Is not inquiry the cure of ignorance? 
عَبْدَ اللَّهِ بْنَ عَبَّاسٍ، قَالَ أَصَابَ رَجُلاً جُرْحٌ فِي عَهْدِ رَسُولِ اللَّهِ صلى الله عليه وسلم ثُمَّ احْتَلَمَ فَأُمِرَ بِالاِغْتِسَالِ فَاغْتَسَلَ فَمَاتَ فَبَلَغَ رَسُولَ اللَّهِ صلى الله عليه وسلم فَقَالَ " قَتَلُوهُ قَتَلَهُمُ اللَّهُ أَلَمْ يَكُنْ شِفَاءُ الْعِيِّ السُّؤَالَ "
This hadeeth, showing the Prophet's great displeasure, if not anger, at the companions implementing 'enjoining the good and forbidding evil' without regard, clearly states that the ability of one to act on one's opinion of 'amar maaruf and nahyil munkar' is not absolute, but rather subject to limits.
This same hadeeth also suggets that these limits are indeed the 'higher purposes/obejctives' captured within the concept of Maqasid al-Shariah: in the case of the above hadeeth, the preservation of life.
We can also see these considerations in action in other instances in the hadeeth and sunnah. This includes the Prophets decisions in regards the treaty of Hudaybiyah  where the companions saw the 'Umrah to Mecca as the right thing to do (mandated, among others, by the Oath/Pledge of Ridwan ), and for some, at all costs (a common approach towards 'amar al-maaruf'), and yet the Prophet refrained.
This act helped secure peace for the Muslims, political power for the Prophet himself as well as the city-state of Medina, brought even more people towards Islam, and led to more peace treatises for the muslims. These aims and objectives are all captured across the several 'higher objectives' of the Maqasid al-Shari'ah. Indeed, for many sahabah , Allah later described this treaty as successful, and hence the correctness of the approach per se, by the verse in Al-Fath:1:
إِنَّا فَتَحۡنَا لَكَ فَتۡحً۬ا مُّبِينً۬ا (١)
Truly We have granted thee a manifest victory (1)
Considering the above, it is clear that the right to enjoin join good and forbid evil is not absolute, but rather subject to considerations of the higher objectives of the Maqasid al-Shari'ah, which itself are consistent with the rights of all mankind.
 Sunan Abi Dawud. Book of Purification (Kitab Al-Taharah)/كتاب الطهارة: hadeeth 337, at https://sunnah.com/abudawud/1/337, accessed 02/05/2020
 in the Tafseer Ibn Katheer:
Abdullah bin Masud and other Companions said, "You consider the conquering of Makkah to be Al-Fath (the victory), while to us, Al-Fath is the treaty conducted at Al-Hudaybiyyah.'' Jabir (bin Abdullah) said, "We only considered Al-Fath to be the day of Hudaybiyyah!'' Al-Bukhari recorded that Al-Bara' (bin Azib) said, "You consider Al-Fath to be the conquest of Makkah, which was indeed a victory. However, we consider Al-Fath to be the pledge of Ar-Ridwan on the Day of Al-Hudaybiyyah".