We should differentiate between religious myths and secular spiritual ideas.
Why?
I'd be more interested in 'how'. In what functional way is 'secular spiritual' any different to 'religiously spiritual'? It's still reliant on just accepting claims without evidence. Religion is just what you get when enough people accept the same unevidenced claim.
We have RED's and documented reincarnation cases. Instead of laughing away such phenomena they should be evaluated.
We have documented claims of these, whether that's what they are remains to be seen. I'm intrigued as to how you suggest we should evaluate them given that, apparently, you believe...
These phenomena are beyond the tool box of science
If, as you suggest, they are observable phenomena I'm intrigued as to how you think they are 'beyond the tool box of science' (I'm going to agree with the majority here and disagree with your assertion that this is a fair interpretation of what Eagleman had to say, at least in the video you linked).
How are any observable phenomena beyond science? Your claims of non-corporeal causes might be beyond science - if so, how do you suggest 'instead of laughing away such phenomena they should be evaluated'? How do you evaluate something that apparently leave no trace? How do you link an untraceable cause to an observable phenomenon through an untraceable mechanism? What's your methodology? How do you validate it?
In what way is just accepting the claim because it's technically not explicitly impossible any different from, say, just making shit up?
O.