According to the nyaya-scripture; race, caste, or species, is invariable.  However, caste distinction, mentioned there does not refer to the difference of caste among human beings born in different countries.  This term refers to the difference of species, such as that which is found between cows, goats, and human beings.

Nyaya – (Sanskrit: “Rule” or “Method”) one of the six systems (darshans) of Vedic philosophy, important for its analysis of logic and epistemology. The major contribution of the Nyaya system is its working out in profound detail the means of knowledge known as inference   Like the other systems, Nyaya is both philosophical and religious. Its ultimate concern is to bring an end to human suffering, which results from ignorance of reality. Liberation is brought about through right knowledge. Nyaya is thus concerned with the means of right knowledge.

Yes, there is a distinction between the castes; however, that type of caste distinction is not eternal.  Human beings have only one caste distinction, which in this case means “species”.  Within the human species, many different caste distinction, have been invented, based on the differences of language, country, styles of dress, and skin color.

Jivas are born into higher or lower varnas, castes, according to their previous karma; and in congruity with their castes; they are eligible for different types of work.  Brahmanas, ksatriyas, vaisyas, and sudras are the four castes.  All others are considered low-born and outside the caste system.

Varna — one of the four Vedic social-occupational divisions of society, distinguished by quality of work and situation with regard to the modes of nature (gunas, comprising the modes of Goodness, Passion & Ignorance

Brahmanas – Are the intellectual class and their occupation is hearing Vedic literature, teaching Vedic literature, learning deity worship and teaching deity worship, receiving charity and giving charity.

Kshatriya – The warrior who is inclined to fight and lead others. The administrative or protective class.

Vaisya (Vaishyas) – Member of the mercantile or agricultural class.

Sudra – The laborer class. He They are meant to render service to the three higher classes, namely the brahmanas, the Kshatriya, and the Vaisya

Vaisnavas are those who have pure bhakti (devotional service to the Sri Krishna); and all human beings are candidates for vaisnava-dharma.  Muslims/Christians/Jews are not eligible to perform the duties prescribed for the different varnas in the varnasrama (the system of four social and four spiritual orders established in the Vedic scriptures and discussed by Çré Krishna in the Bhagavad-gita.)

 system because their birth disqualifies them.  However, they have every right to participate in the practices of bhakti.  One can never say that he knows the actual purport of the scriptures until he has minutely examined the subtle differences between Work, Knowledge, and Devotional-Service to Krishna.)

When one performs one’s prescribed karma, work, the heart is gradually purified so that one becomes eligible for jnana, knowledge.  Amongst the jnanis, some advocate the undifferentiated impersonal brahma, while others are Vaisnavas, who accept the personal form of Bhagavan (God, Sri Krishna) possessing transcendental attributes (concerned with the a priori or intuitive basis of an independent of experience (existing or coming before in time, place, or sequence, surpassing all others, superior, beyond common thought or experience, mystical or supernatural.)