It sounds like a bunch of bunk to me.

I am spiritual but not religious. Confidently and comfortably so. Religious means belonging to an established religious order. I do not. Spiritual means feeling a connectedness with...the Universe (or whatever you want to call it).
Your journey leads you to believe it's woowoo. My journey has led me to providing end of life care for the dead and dying and now those less fortunate in the later stages of life who need to know someone cares and will help keep them safe. You don't arrive at my destination in life without having some sense of connectedness to...the Universe, the greater good, the description birdingnut provides. My experience is deeply spiritual and incredibly fulfilling.

It means that even though you no longer believe in Christianity, the Bible, or the Hebrew god, you still believe Einstein and the Law of Thermodynamics, which says we are all made of energy, that time and space are an illusion, that energy can't be destroyed or created, therefore we have always existed and will always exist, in some energy form.

Also, there is the well documented research into children aged 2-6 years old who remember past lives in such great detail, they can be independently verified.

It means you are really an atheist but still want to get girls!

It is all woo woo

It means they believe in magic and promote magical ideas that exist within theistic beliefs, without themselves being labelled as believing in or following a particular god.

It means an atheist who has not incorporated skepticism. Atheism without skepticism can still leave a person open to woo woo ideas.

Religious means you believe in magic invented by others. Spiritual means you make it up yourself.

I think that's just what you say on a dating site when you don't want to say you are an athiest.

For me, claiming to be spiritual is a cop-out. Woo woo indeed. Atheists can feel awe. Atheists can feel at one with nature and/or the universe. Atheists do not need to give up one iota of their rationality along with religious/spiritual belief. Spirit? Soul? I suppose we all have the same amount of whatever that is, which is probably nothing at all, probably a convenient metaphor for not being a robot without feelings.