Even when a claim is made respectfully, it's still a claim. There are very few religions that say "I think this may or may not be true; I lean a bit towards 'true' (even though it's just as likely that I'm wrong), so I'll build my life around the idea that it's true." Most say something like "I know in my heart of hearts that THIS is true, even though I respect the fact that the beliefs of people who don't acknowledge this 'fact' are still meaningful and important to them, and may have been arrived at honestly and intelligently."
... and there are plenty of religions where the truth of their beliefs is dependent on the truth of facts about physical things. For instance, every single revealed religion is based on the idea that an event occurred where their god/gods/angels/whatever transmitted the revealed knowledge of their religion into a form in the physical world (whether this was stone tablets/scriptures transcribed by a prophet/oral tradition/golden plates/etc.).
But can you give some examples that aren't dependent on objective truth claims? I can't think of any.
Not revealed religions, no, but most religions aren't revealed; most are indigenous. Thus, most religions don't actually deal in belief much, if at all. They're intimately tied into the lifestyles of their cultures. So if you're asking for examples of religions, revealed, indigenous, or otherwise; that I *know* aren't dependent on objective truth claims, well...
Celtic Reconstructionism
Heathenry
Hellenism
Religio Romana
Rodnovery
Shinto
Shen Dao
Daoism
Vedanta
Shaktism
Most Hindu religions, actually, except for a few that gainted popularity in the West.
Buddhism
Wicca and its descendents
And I'd be willing to bet that the vast majority of religions still practiced by unbroken Tribal cultures all over the world would qualify, as well.
That's not to say groups or individuals within these religions don't sometimes make objective truth claims, but your inquiry is about depdendence, not presence. I'm sure there's others I've either forgotten about or just don't know about.
yeah well...I was just responding to your post.....it was headed to digression...
and yes we are headed to extinction.
No more than anything else ever. Everything dies sooner or later, so in other news, Heaven is blue and cows go moo.