It is jatidharma that goes to make the inner guna (inner quality or nature) of an individual. So Sri Krsna's dictum in the Gita that the caturvana division is in accord with the gunas and the idea that the caste is based on birth are one and the same. There is no conflict between the two. You cannot find fault with Sri Krsna for his practice being at variance with his precept.
Parasurama and Dronacarya were Brahmins but they were Ksatriyas by nature. On the other hand, Visvamitra, a valorous Ksatriya king known for his violent and passionate temperament, became a Brahmin rsi. Cases like this are extremely rare, and are exceptions to the rule of jati dharma. On the whole we see that the Lord functions on the basis that, whatever be the outward qualities of individuals, their inner quality is in keeping with their hereditary vocations.
How can birth be the basis of the quality on which one's occupation is based? Before a man's individual character develops, he grows in a certain environment, the environment evolved through the vocation practiced in his family from generation to generation. He adopts this vocation and receives training in it from his people. It is in this manner that his guna is formed, and it is in keeping with his work. Everybody must have the conviction that he is benefited by the occupation to which he is born. When people in the past had this attitude in the past they were free from greed and feelings of rivalry. Besides, though they were divided on the basis of their vocations, there was harmony among them. Children born in such a set-up naturally develop a liking and aptitude for the family vocation. So what is practised according to birth came to be the same as that practised according to guna. Whatever the view of reformers today, in the old days an individual's ability to do a job was in accord with his guna; and in the dharma obtained in the past a man practised his calling according to his guna. Now it has become topsy-turvy.
What is the view of the psychologists on this question? According to them, heredity and environment play a crucial part in determining a man's character, abilities and attitudes. In the past all vocations were handed down from grandfather to father and from father to son. Besides, each group practising a particular occupation or trade lived in a separate area in the village. The Brahmins, for instance, lived in the agrahara and, similarly, each of the other jatis had its own quarter. So the environment also helped each section to develop its special skills and character. These two factors - heredity and environment - were greatly instrumental in shaping a person's guna and vocation.
Instead of speaking about the subject myself, I will cite the views of Gandhiji who is much respected by the reformists: "The Gita does talk of varna being according to guna and karma, but guna and karma are inherited by birth." So the fact that Krsna Paramatman's practice is not at variance with his doctrine is confirmed by Gandhiji. Modernists should not twist and distort the Vedas and sastras and the pronouncements of Krsna Paramatman to suit their own contentions.
Krsna is usually imperative in his utterances. "I speak, you listen," such is his manner. But when he speaks of people and their duties, he does not inpose himself saying "I speak thus", but instead he points to what is laid down in the sastras to be the authority. During Krsna's own time the various castes were divided according to birth: we learn this, without any room for doubt, from the Mahabharata, the Bhagavata and the Visnu Purana. I mention this because some research scholars today are likely to put forward the view that caste based on birth evolved after the time of Krsna. The epic and the Puranas mentioned above declare categorically that during the age of Sri Krsna Paramatman the sastras dealing with varnasrama were the authority for dharma. It was at such a time, when an individual's vocation was determined by birth, that the Lord declared in clear terms :
Yah sastra -vidhim utsrjya vartate kama-karatah
Na sa siddhim avapnoti na sukham na param gatim
Tasmacchastram pramanam te karyakaryavyavasthitau
Jnatva sastravidhan oktam karma kartum iha'rhasi
-Bhagavadgita, 16. 23 & 24.
Who so forsakes the injunctions of the sastras and lives according to his own desires does not obtain liberation, finds no happiness. (The Sastras determine your work, what is right and what is wrong. You must know the way shown by the sastras and pursue the work - vocation - according to them.)
Sri Krsna establishes that an individual owes his caste to his birth. There should not be the slightest doubt about it.
For a general background, please see here