Not entirely accurate. Any 15th century lower caste or untouchable Hindu in India had very strong incentives to convert to Islam.
In Islam, at least in theory, there is no such thing as caste or even class. In traditional Hindu society, there is absolutely no way to rise above your "place" in life.
Actually, in traditional Hindu society, before the influence of Muslims (say 1500 years ago and more), caste was not carved in stone; it was more a social system based on ability and qualities; not solely on birth. If you read the source documents that is quite clear.
There's a word - brahama bandhu, or kshatra bandhu - that means "friend of a brahmin" or "friend of a kshatriya" indicating someone born into a particular caste or social order but not qualified as such.