My apologies, I didn't read all of it as I am extremely tired atm and about to take some nap, but I'll answer some inquiries brought up by Deeje:
For those who think of themselves as “spiritual”....what does that actually mean in real terms?
To me personally, spirituality is the studies of the spiritual laws of nature [like karma] and morality. And the ultimate purpose of spirituality to learn about these spiritual laws, restructure your life in such a way where you leverage these laws to your maximum advantage to live a spiritually healthy and morally upright life, and to develop and implementing justified, true morals through moral reasoning [another aspect of spirituality]. The end result of spirituality is achieving and maintaining peace within, in your soul despite of many internal pressures [the pressured exerted on your soul by your greed, your lust, your pride, your fears etc. etc. etc.] and peace with the outside world, despite the pressure exerted upon you by the world and the hardships in it, while living a spiritual healthy and morally upright life in this state of peace.
Being spiritual means you are a practitioner of spirituality, and your main objective is achieving all the tasks described above and whatever spirituality entails.
You don't let any specific school of thought you bound you. You study them critically, find out what is beneficial and [most likely] true, and embrace it, and whatever is useless and [most likely] false, is discarded. Most important, you do experiential learning, for our personal experience are only [relatively] most reliable source of information. Books and religions are other's opinion we take for grant. History is, more or less, bunk, for it is someone else's personal perspective of something that happened we can't even verify [in short, history is HIS-STORY]. Your personal experiences is the only most trust-worthy friend in the world of lies and deception.
Whatever we learn through our experience [after healthy assessment of our experience, of course] is incorporated in our school of thought. And spirituality, much like science, is a self-correcting field. We keep on learning, discarding the outdated beliefs [and such things], and it keep replacing it with more polished and relatively better one which have a better explanatory power, is practically beneficial, further solidifies the other [well-vetted] spiritual beliefs, and gives spiritual results.
Not what appeals to us, but rather what is pragmatic. I believe in the whole of Qur'an, also what I remember of Bible, Jewish scripture [which I didn't read most and forgot quickly] and also Hinduism. The only thing we discard is that which provides zero spiritual benefits. I discarded "Hajj" from my spiritual life as I believe it is vain, non-beneficial and useless, and it seems like it was only meant for those specific people [Beduoin arabs] of that specific era [7th century], just like the whole Qur'an. What is still applicable and beneficial in the Qur'an, I incorporated in my spiritual belief-system, like charity, taking care of orphans and those in need etc.
God is too Supreme is even care about insignificant advanced-bacterias like us. God has created an automatic system with spiritual [and physical] laws acting in us, and taught us about that. And He just warned us not to go against these laws that'll lead you to your destruction, just like any sensible parents teaches their children not to go against the law of gravity in your attempts to act like Superman or you'll hurt yourself. God has shown us a system of leading a life where there are practices that ensures that we leverage all the spiritual laws and have moral conditioning to lead a spiritual healthy and morally upright life, along with some spiritual truths.
True God doesn't require anything. God doesn't need anything from us, we need God. We require God, God is to supreme to demand anything to those immeasurably inferior to him. God is like a teacher, he teaches how to safely tread the line of righteous path, and not fall into evil.
We just don't our thinking to be bogged down with one specific dogma. It's like looking at things with only one perspective, there are many other perspectives. And to develop the most perfect philosophy, we have to keep all the differing views and perspective, and create in personal views in light of them. Religion is like "my perspective is the only right perspective, just keep looking at things my way or you're a infidel."