God, by definition is not immoral but the very definition of morality.
However, man is incredibly immoral and he is determined to seek justification for every horrendous deed he has ever done. So, in the OT we have man ascribing all sorts of evil motivations and actions to a God he doesn't quite understand.
In the NT, we have God become flesh and he came to set the record straight. "I desire mercy and not Sacrifice!" "Love your neighbor as yourself." are given to us and frankly the whole idea that there aren't a bunch of laws frightens us. So much so, that we take the first opportunity to crucify God.
So, did we invent God? Are there TWO Gods? Is God schizophrenic? No, it's not God who is changing: it's us. Just as we evolved from a one cell organism, our society is also evolving. We were once quite tribal and so our views were such. We defined God in terms of being a tribe. Today, we have a more global view, and yet we seemed determined to judge God by the writings of a few tribesmen. Go figure.