Also Jesus was born in a poor family, which would have made him a lower caste hindu if he was born in India
This is not really true. If I recall correctly, Jesus was born in the Davidic line as per the bible, which was important for his claim as the messiah. His high "caste" did matter to his followers. Caste is determined by your pedigree, and not by how rich you are.
It's true that caste-based discrimination is a curse that India must do away with. Perhaps it'd be more helpful to let different communities adhere to whatever traditions are important to them without attaching the concept of highness or lowness associated with it.
Not considering hiring people with non-Biblical or clearly "Black" names is one of those things which you can't see. Not showing Black people houses in good neighbourhoods is another. That behaviour is still racist, but invisible.
Casteism plays out along similar lines, with people not being hired, or promoted.
The term implies facing the wrong way
The irony is that there are some upper caste people fighting to classify their class as backward because they have quotas in govt jobs/education.
You see, eons ago, caste in Indian society was not right, it was your job (warrior = Kshatriya, scholar = bramhin, trader = baniya, labourer = shudra).
The first three called themselves upper class and the last one was the lower class.
Among the first three, the first one think that they're upper than the other two. The second one thinks that they're upper than the third.
But this was never hereditary. if you were born to a Bramhin (basically any person who had the brains to be a scholar) and if you didn't have the knack of being a 'scholar' you could become a warrior if you had the skills, or a trader, if you had those skills. If you had no such skills then you were the labourer.
But what happened is, centuries after this tradition started, it was made hereditary. So only sons of Bramhins can be scholars, only sons of Kshatriyas can be warriors, only sons of Baniyas can be traders and all Shudras were forever shudras.
The architect scholar and almost superman historical Dr Ambedkar was a Mahar aka Dalit aka Shudra. This guy graduated at the top of LSE, has written extensively on India and almost all of his writings were 100% spot on (his thoughts about why it was good that Pakistan formed for Indian Army's balance or what'll happen when Hindu nationalism will rise etc)
But he was treated as shit just because he was born a Mahar.
Now the tragical thing is that Mahars were warriors in Shivaji Maharaj's time (he was a Deccan King who was kinda democratic and not cruel like Mughals. Even actual Gods are below him in my state, people, including atheists like me worship him, not in temples obviously. It is like you can insult Gods and it'd be fine but if you insult him then you are done)
During his reign, Mahars were fierce warriors and had their own regiment in his army. But his descendents weren't exactly great and in the 3rd generation king's army, only 'higher caste' khastriyas could be warriors and others were treated as literally shit. there has been documented evidence (thank God for the documentation) that at the end of the Peshwa rule, the lower class people had to attach a broom at their backside so that they'd sweep the land they walked on because they were considered 'filthy' (not physically). No lower class man or woman or child was allowed in upper class wells, temples. they were not allowed to have horses in their weddings etc. Some of these practices are still rampant in India where upper caste privileged people are blind. you can see quite a few in this thread who are either blind or racist.
basically this was just like slavery without higher caste people owning the lower caste people.
My knowledge of India is very basic. I have indian friends and coworkers and have never thought about this being part of their story.