Since one of religions dominant roles in society has been to set a moral compass that all agree on, it makes sense that people without a religion would be searching for new ways to understanding morality.
But that doesn’t mean spirituality is inherently without a moral system.
The idea of being a “spiritual” person rather than a “religious” person may mean that a person subscribes to many doctrines rather than just one.
I myself subscribe to the scientific method, Buddhist dialectics, Buddhist rituals/sutras/tantras/precepts, some Christian thought, and also pagan and animistic beliefs from North America, Scotland, and Japan.
You can see, a person like me draws from many sources, none of which I think are inherently, 100% correct—especially not for anyone but myself.
Because of this, I think I have a firm base of morality to stand on when thinking and going about my daily life. Which may be an illusion.