It is quite possible that it is devoid of any relationship to the god you describe. And that is a good thing as far as I am concerned.
God does love you. God does care about you. God does offer you the gift of eternal life. This is true of everyone. The problem isn’t God. It never has been. The problem is that it remains our choice whether to accept the gift or not. But Jesus and Paul were also quite clear that entitlement does not work.
Primarily I speak of the Gnostic gospel of salvation by a secret knowledge such as correct doctrine, which I have heard affirmed numerous times by people identifying themselves as Christian. What Jesus and Paul taught however is the gospel of salvation by the grace of God. I have no idea whether this has anything to do with denomination or not, but it seems pretty widespread to me.
Well now you know my criterion, it is for you to say according your theology which I assume that you know even though I do not. I am not really interested in making discussions personally like that. I am only interested in the principles.