What do you believe in? Why do you believe it? Were you born into it or did you change your beliefs as you came upon it? Is it mutually exclusive of other viewpoints and beliefs, or is it inclusive and expansive with them? The two words: conversion and initiation used in a religious or spiritual context have subtle differences in meaning. They both usually refer to coming to a new religious system or belief, but they depart from there.
When I was first introduced to Hinduism, I was told it was something people can’t convert to. At the time my 20-something brain said to me, don’t tell me what I can and cannot do; I was put off. Whenever I’m told there is something I can’t do, my first reaction is gut-wrench abhorrence to the idea: why not? Whether the statement itself is true or not, the answer underlying it is rooted more in philosophy and perspective than mere facts. My current understanding is: you can’t convert to Hinduism, but you can initiate into it. The difference seems subtle, but the meaning is very important. (I’ll leave caste aside.)
Most of the dominant Western religions [Judaism, Catholicism, Islam] have a conversation aspect to them. You shed your previous beliefs and proclaim you now have taken on the new dogma. You are converted. You now believe what the others believe. Of course there are variances. Not all people from a religion are generic and believe the same things wholeheartedly, but the conversion takes place and in doing so you proclaim your faith in the new dogma and doctrines. The door closes on your past belief system. These systems are usually exclusive in their beliefs with the religion you converted into.