"Would an Abrahamic God Deserve Our Forgiveness?"
No, to be quite honest.
The deity described by the bible (*particularly* in the Old Testament, but even the New isn't without references) is a bigot, a sexist, and absolutely a murderer...to say nothing of his vanity, ego-centrism and general lack of a moral center.
Here is a being that supposedly creates mankind, flaws and all, then somehow gets insulted when man acts *precisely the way he knew they would when he made them* and then uses that as an excuse to require us to be "forgiven" for character flaws he instilled in us in the first place.
In other words, we are punished for mistakes he knew we would make, and indeed designed us to make.
To top it off, his punishment runs even deeper by banishing anyone who doesn't believe in him to an eternity of burning pain and suffering. This is the mentality of a 4-year old. Anyone ever see that old Twilight Zone episode with the kid banishing people to the corn field for making him upset? Same deal except probably worse.
Then he attempts to hold everyone hostage emotionally by sending his "son" to "die" for our sins, claiming that this is the only way to forgive us (nevermind that he ostensibly created the universe and thus *makes the rules*...no, no, this is the ONLY way for some reason) and brow-beats us with this "sacrifice" over and over again. "Look what I did for you!" he says, "I sacrificed my son for you!". Never mind that this was no true sacrifice at all, since Jesus then apparently rose up and now is sitting pretty in heaven (and he was also god at the same time? Whatever, a wizard did it). So, what did this god actually sacrifice? He didn't get to see his kid for 3 days? Sounds terrible.
Suddenly the entrance requirement to his afterlife clubhouse changes though: Now you have to believe that his son died for you, and if you don't then prepare for eternal fire and the worst 3rd degree burns you've ever had, buddy!
The Abrahamic god is a rage machine. A jealous, homicidal maniac that displays all the winning traits of alcoholism, sociopathy and bi-polar disorder at the same time. One might think that impossible, but hey, with god, all things are possible, right?
Luckily, I don't believe that deity exists, so we don't have to worry about it.