It mostly doesn’t. Historically there have been lots of mass conversions to other religions the first one being Buddhism in 600BC. Buddhism came about primarily as a response to Hindu orthodoxy and the caste system.
AFAIK, it did not. It came about from the Buddha's teachings, which were not about caste, but about suffering and its cessation via attaining nirvana (but I am not an expert on Buddhism; we only learned some about it in school).
My guess is that, instead, later, many people may have converted to it, maybe some due to orthodoxy.
I am talking about olden times. In recent times, neo-Buddhists definitely may have converted due to the caste system. I have read something about that earlier. See Dr. Ambedkar.
Your above point itself proves what I said: "dueling literature"! Heh.
Groups like the Veerashaivas were concertedly anti-caste discrimination but the Buddhists were decidedly not. They’d be more like a Kshatriya revolt against Brahmins but that’s just upper-caste infighting, not anti-caste. Similarly with Muslim and Christian converts, the first ones were predominantly, if not almost entirely, Brahmin.
This is a modern myth, that has been proven to be grossly untrue, time and again.
Buddhism was a mostly upper caste phenomenon.