Ancient Varn system

Chapter 4 text 13

cātur-varṇyaṁ mayā sṛṣṭaṁ
guṇa-karma-vibhāgaśaḥ
tasya kartāram api māṁ
viddhy akartāram avyayam

TRANSLATION

“According to the three modes of material nature and the work associated with them, the four divisions of human society are created by Me”. 

Varna means duty or occupation, he clearly mention   that he devided (vibhāgaśaḥ) this society based on " Gun and karma"(guṇa-karma) not by birth !!

     It means son of lawyer would not be layer, he is  a lawyer  if  has  a quality (gun ) and he   practice ( karma) Law, same way a son of Brahman is not a bhraman if he does not have a quality of bhraman  as well  he  don’t practice the way brahma should practice or behave!!similarly for all Khastriy and Vaishya !  That is how varnavyavastha is been Developed by Krishna 

Now how each should behave? 

Brahman: situated in mode of goodness, never work under any class, behave as a advisor/guide for the society, because they are independent , their advise is independent! their role is to advise without fear and motive!  for reference  take a ex: king vena from bhagvatam ,and chanakya , bad example is in Mahabharat, Guru Dron was accepting favor from dhutrastra that’s a reason he could not chose his side independently

Kshatriyas : Is the administrative class, technically called the kṣatriyas due to their being situated in the mode of passion. they are protector and maintainer, their role is protect and manage brahamans , Cows and Citizens of the kingdom,  Best ex: King Ram, King Yudhisthir, King Dashrath

Vaishya : The mercantile men, called the vaiśyas, are situated in the mixed modes of passion and ignorance, they are businessmen, their role is to do farming, take care of cows and feed the society. best ex: Nand maharaj

Shudra: They are in a Mode of ignorance, they are motivated by sense enjoyment, they cannot think beyond their own self /Family one !! that’s a reason they are classified as shudra they cannot take any other role as  Brhaman, Khatriya , VAishya, as all other class need sacrifice and motive  to serve society, as a Bahaman Chanakya advise Dhanand boldly without any fear, he sacrifice his life to developed Chandragupt for the welfare of Bharat,  King ram as a kshatruya Sacrifice his wife to give  a priority to Raj Dharma above to his self /family ,  

Since they donot have quality of any of these three varn they classified as Shudra, Shudra is not a cast it’s a Designation, their role is to serve all these three classes and return they will get paid/salaried/maintained by three class, and non of upper class would exploit or harm them, in the explanation you shared, didn’t say you should not give respect, respect is irrespective to the class or birth and should be given to all, yes but since they are shudra they should not expect any respect! If Sudra try to take a charge of anyof this varn that’s a havoc as they will exploit that workor work ethics by kepping self /family in center, so they cannot think beyond themselves ! Ex: Drona Charya ask a Dakshina from Eklavya, Its not because he was shudra its because he do not have a  quality of discrimination ! Kshatriya is not just who is skilled in Archery, He accepted friendship of Duryodhan without discrimination, he accepted based on his self-interest /favor/under influence of duryodhan,

These entire Varnavayvastha is functioning so well and that’s a reason india or bharat varsh was flooded with prosperity and happiness,  Recently the major society is dominated by shudra,  As Majority cannot think beyond our family and food! So the  politician whom we  vote! They come to power to build their bank balance ! as shudra cannot think beyond sense gratification, that’s a reason when the society is ruled by shudra there is a havoc !

And Krishna Consciousness  is beyond these, its an aid to transcendent any Varna or Ashram, the society structure was  arrange in such a way that every citizen get an appropriate time to practice devotional service but in current age, its shudra driven society because its based on Sense gratification!! People work day and night  for the instrument of sense gratification  and they being ignorant, forgot the motive of life and that is to  attain Spiritual word

As well Please Refer .Bhagvat Geeta AS IT IS, it will help you to understand more logically.