In my experience, at least in the US, non-denominational when associated with an institution generally means “Christian” but not affiliated with a sect. They’re (typically) still quite Christian, and the phrase can be and is applied to churches ranging from the ones flying Pride flags and declaring that they’re open to everyone to ones like Westboro - some of the most radical Christian churches are non-denominational because their views are too conservative for even the more conservative right wing religions.

The phrase itself is an organizational status and does not indicate what kinds of beliefs a person has. It’s not unlike someone describing themselves as “politically independent.” You don’t know if they’re Greenpeace types, libertarians, or far right of the republicans.

Edit: The usual term in the US for what I think you’re describing is “Spiritual, but not religious.” That’s the way it’s usually written in census and survey forms.