I don't see our religions surviving robots and serious climate change and fucking everything else. Seriously, you can't just fold that into the bible. It's just too chaotic.
Since you mention the Bible specifically here, I'll just mention that the Abrahamic religions have survived literally thousands of years of change, and it hasn't stopped anyone from folding things into their beliefs. Can't speak to any detail of anything outside of them.
Hardliners will just double down on their beliefs. I know some people who think that even believing that climate change is real is paganism, for example, despite all the evidence. If climate change became undeniable, like say flooding Florida, well, that's just God's will and you don't question it past that. That's what Hurricane Katrina was, anyway.
People who aren't hardliners may be more reasonable and say things like God left Earth in our hands and we messed it up because we're fallible humans. Of course we messed it up. <dwarf fortress>It was inevitable.</dwarf fortress>
On the topic of AI and robots, I'm pretty sure hardliners will just say they're soulless machines and we'll incur God's wrath for trying to create life (hey, convenient explanation for climate change getting worse). More reasonable people may say that anything that can understand the Bible has a soul and can be saved. I'm sure some Christian denominations will eventually take that route. No idea how other religions would handle it.
So in short, I'd expect a lot of the same with a generational shift toward just massaging beliefs as needed. The literal contents of the Bible or any other holy book are only tangentially relevant. It doesn't matter if someone's Roomba woke up tomorrow and started asking them if it had a soul, I can't see mainstream religions changing quickly. It's too core to people's identity.