Are we promoting casteism?
Caste is an English word derived from the Portuguese word "casta", meaning racial lineage.
The "Casta System" was created by the Portuguese and the Spaniards to control other racial groups and maintain their power and superiority. Under the Casta system, the occupation or work of people and their identity were imposed on their descendants from birth. Meaning a sweeper's son will be sweeper, a carpenter's son will be carpenter and so on.
Taking inspiration from these, the British imposed the "Caste System" on us Indians in the form of the "Caste System" to divide Indians among themselves. The British introduced the caste system in India on January 4, 1844, and in 1881 caste census of India was done.

Image: Casta System painting by Ignacio María Barreda, Year 1777 (Source - Wikipedia)
We Indians today, by adopting this caste system, are continuing the terrible mistake of deciding the caste of our children right from birth.
For example, a teacher (Shastri, Acharya) is called an oil producer or a businessman of oil (Teli). A leader (King, Kshatriy), is addressed as the one who extracts salt from the Noni soil (Nonia).
Jati means type, kind. (Flexibility in Identity)
Jati is determined by you when you want to identify yourself with a particular type of skill. Add it to your name to inform others about your skills. Like people add Doctor, CA, Advocate, Engineer, etc with their name.
Jati is also a noun for a group of people proficient in a particular skill. Jati can be changed as per your wish.
If you learn a different skill or choose a different profession. For example, a fisherman (Machhuara) who becomes a hair dresser he will be called a Hajam (Barber) or a software engineer who starts doing fish farming will be called a Machhuara
There was Jati system in India but it did not fix one's Jati like casta system, rather like today's time there was freedom to choose one's skill and work.
The Jati of a person cannot be decided by birth.
His skill or talent will decide his caste. It should not be decided on the basis of caste of the parents at all. It will be such that a person born in a doctor's house will be called a doctor, even if he is a civil engineer.
What is Varna? (A Framework for Functionality)
Varna means the nature, and qualities of a person which define their character.
And the basis of the Varna system was Karma or Guna. The basic purpose of the Varna system is to create a functional division of society. Because if a person works according to his nature, then he does the work correctly.
The interesting thing is that in the 17th century, the division of labor propagated by Adam Smith is highly appreciated, which is another form of the Varna system. Whereas the Varna system is blamed wrongly.
"We believe all the Varnas are within you."
You are made of a combination of all four,
The truth is that we keep changing between these four characters from morning to night!!
For example, Shri Krishna was a Brahman when he gave the knowledge of the Gita, he was a Shudra when he drove the chariot for Arjuna, he was a Kshtriya when he killed the demons or became king of Dwarka, and in childhood, he was a Vaishya as a cowherd.

Brāhman Krishna

Vaishy Krishna

Shudr Krishna

Kshtriy Krishna
Similarly, you are a Brahman when you study and teach, you are a Kshatriya when you protect your family, you are a Vaishya when you manage your household, and you are a Shudra when you clean the house.
Don't associate yourself with any caste just because the system created by the British government still decides your or your child's caste even before birth.
Hope you have got the answer to the question of Sanātman being casteist.
Let's reject caste, adapt the qualities of Varn, Eradicate discrimination and unite Sanatan.