The conflict as I see it is between the philosopher’s and the folk’s gods. So I get to define it that way because that’s how I see it. The former god is an abstraction, conjured by reason, while the latter one is an invisible friend conjured by the fear of death.
But if you want to focus on the meaning of “person,” that’s fine. Theism’s incoherence is overdetermined, so there’s no shortage of confusions and embarrassments there to be found. Not only do people have bodies, as far as anyone knows, which the First Cause couldn’t have, but people also have personalities and mental limitations. Also, a person’s mental states come one after the other because people are subject to time. So the notion of a person “existing” outside of space and time is a nonstarter. What theologians do is extrapolate from psychology and social studies to arrive at the idea of an ultimate, transhuman or super person. This is the omniscient, omnipotent, omnipresent, omnibenevolent divine being.
And the more you analyze that concept, as philosophers are wont to do, the less personal this being seems. The super being turns out to be just the First Cause, an immaterial “substance” or absolute ground of being, not a living, conscious, intelligent thing. As soon as you emphasize its personhood, you’re left with all the awkward but perfectly fair questions of how this person could have arisen with no parents, what this person’s gender is, or how this person could avoid becoming insane by having all its thoughts happening at once.
Monotheism makes God’s personhood nonsensical, which means this development of religion leads implicitly to secularism and to atheism. See the articles below for politically incorrect analyses of God’s personhood, and for more on monotheism’s role in religion’s implosion.