Hmm. I wonder if 24th-century Hindus consider Surak to have been an avatar of Vishnu...
I don't know if this is a joke but I think it's an interesting suggestion. Ultimately I'd have to say that it's unlikely, but it's really impossible to predict how specific religions would involve.
It's not a joke. I've heard that there are some Hindus who consider Jesus to be a possible avatar of Vishnu, or at least that Jesus's unchronicled adolescence and adulthood were spent in the Subcontinent learning the ways of peace and enlightenment from Hindus. Hinduism is historically a very inclusive syncretic religion; indeed, the very name "Hinduism" is something of a Western imposition, a simplification of a whole range of diverse and freely overlapping belief systems. So there's little difficulty incorporating elements of other religions or cultures into Hindu belief.
I was raised Muslim and Muslim's are to pray at certain times, based on the position of the sun, and towards Mecca. I wonder how this would work in space, especially on a starship thousands of light years away from Earth.
I've researched that question for my own writing, and my understanding is that such practices are considered traditional, not obligatory. Facing Mecca is considered an aid in focusing the mind toward God, but if you don't know where Mecca is, it's enough to focus inward, since God is inside everyone. Or something like that. Generally, Islam is pretty willing to make exceptions to the standard practices, and only ask what you're practically capable of delivering. (For instance, you're expected to make the hajj, but only if you can afford to, are healthy enough, etc.)
Although, of course, it's not that hard to know what direction Earth is in as long as you know your position in space, and on a starship that would be easy to calculate. Muslims on starships could simply ask the computer which way to face for prayer, or carry the equivalent of a GPS device in their pockets.
Indeed...I've always appreciated Star Trek's portrayal of a future in which human beings are not held hostage by the beliefs, values, and limitations of the dead. TNG mentioned an observance of the 'Hindu festival of lights" during "Data's Day", and TOS made a reference or two to Christianity ("Bread and Circuses"), but otherwise it was free from creeds and dogma.
There's a big difference between spirituality and dogma. Organized religions and the proponents of dogma like to claim they have a monopoly on spirituality, but there are plenty of alternative, more individualistic and flexible approaches. It's certainly possible to believe in, or at least be receptive to the idea of, a spiritual essence to the cosmos while still rejecting the doctrines of any organized church. That's pretty much how Roddenberry thought -- not that there was nothing divine in the universe, but that whatever divinity might exist had nothing to do with the dogmas and strictures of any human religious institution.