Yeah exactly, nowadays (especially in the US)... it's not easy to tell what caste a person is from.
If someone doesn't want to share their caste, that's very easy to do.
Hence... discrimination amongst indians is usually around where in india you're from, what language do you speak (tamil, hindi, marathi, etc.), what tier college you went to (IIT?), obviously gender, and other factors.
Comparing Caste to race is completely wrong and it's a red herring.
Having every indian fill out what caste they are on their job application doesn't solve the problem.