If you have a mind that looks for truth both outside of and inside of religions, then what do you call that mentality?
I always have considered that as being a "scientific" outlook, (and I think Richard Dawkins thinks like this as well as myself) but experience has shown that most people insist that science is just as much a limited and dogmatic worldview as religion. So that means such open-mindedness is NOT scientific!
Well, you don't call such a person "religious", and yet they could still be "spiritual" without compromising their postition (and shutting themselves in a box). They may be either: atheist, agnostic or non-religious theist (making it up as they go along) or, alternatively, not any of these labels, because they may feel that the whole notion of how they relate to a God concept is irrelevant to their worldview and reject such a pointless definition. (The latter being my own preference).
Surely, anyone would rather have a mind that can freely explore the smorgesbord of ideas already established, as well as formulate ideas of their own, without any pressure to collect everything into a rigid structure at all. [I suppose everyone would want this in their heart, but few could acheive it - and many, accepting their inability to do so and possible fear of seeing things clearly that scare them, reaslitically take shelter in the security of religious dogma].
You can still have this openness and yet have strongly held opinions. You can be into any kind of -ism even. These sort of ideologies, while they mostly contain dogmatic adherents, who cling to their convictions in the same way that the religious do, are nevertheless viewable as being staging posts, from which you can survey your options of where you might like to go next, if anywhere. Religions, by contrast require that you close your mind to alternatives and rely entirely upon faith.