The creator of the religion (going back to Mormon again) could have misled and lied to what became today's practitioners... I mean, the creation of it, today, sounds so absurd that you have to believe it was a crock... so I'm not blaming the practitioners...
I think Smith was a fraud, but that's not to say anything negative about today's practitioners of Mormonism.
So while it may fit your two factors, could it still be considered illegitimate? Or perhaps we need a different word, if that one doesn't jive well.
Similar with Scientology... it's absolutely a cult, we all see it, we all know it... but those that are deep into it may see it a different way.
Maybe "traditional" instead of legitimate?
Hinduism, even discounting its age, seems legitimate because it carries the badges of what we think of as a polytheistic religion. It is traditional, not just because it has traditions, but because it fits with our concept of what a religion feels like.