Actually, Hindus do have a problem with this. It means yoiu HAVE to proclaims yourself Hindu if you want also to be Christian. That means accept the caste system and not try to persuade caste members to get too “uppity.”
Hinduism is more appropriately defined as a complex of religions and cultures than as “a religion.”
As such, to a very considerable extent each Hindu defines his own religion. While most believe in caste, there is of course the slight problem that someone who converts wouldn’t have a caste, since that is inherited.
Not all Hindus believe in caste or in the need to keep lower caste members down.