The answer is yes.
Gita 18.41
Brāhmaṇas, kṣatriyas, vaiśyas and śūdras are distinguished by the
qualities born of their own natures in accordance with the material
modes, O chastiser of the enemy.
Commentary by Sri Ramanujacharya:
The nature of Brahmanas, Ksatriyas, Vaisyas, and Sudras are due to
their respective inherent dispositions. The meaning is that their past
Karma has been the cause of determining births as Brahmanas etc. The
Sattva and other Gunas are the result of such Karma. The Sattva-guna
is born from the inherent nature of the Brahmana becoming dominant by
suppressing the qualities of Rajas and Tamas. The quality of Rajas
originates from the inherent nature of the Ksatriyas becoming dominant
by suppressing qualities of Sattva and Tamas. Tamoguna arises from the
inherent nature of the Vaisya, becoming dominant in a little way by
suppressing Sattva and Rajas. The duties and works assigned to them
according to the Gunas constituting their inherent nature, are
expounded and allotted by the Sastras in the order described. For the
Sastras analyse that the Brahmanas etc., possess such and such
attributes and such and such are their duties and occupations.
Chandogya Upanishad 5/10/7
“Those whose conduct here on earth has been good will quickly attain
some good birth as a brahmin, birth as a kshatriya, or birth as
a vaisya. But those whose conduct here has been evil will quickly
attain some evil birth—birth as a dog, birth as a pig, or birth as a
chandala.”
If yes, why it is difficult to accept caste system?
Hindus and Hindu organisation nowadays think that because of this system only, we lose Hindu population to other religion.So they don't want this system.