Yeah, it's an ambiguous mess that has created over a thousand different denominations who can't agree on exactly what one must do for salvation, the single most important question in all of existence if true.
I don't worry about salvation. If one's motivation to be a good person is to end up in heaven rather than hell...well, I would question that kind of attitude.
The laws and rules for slavery however, are very clear and not allegory. A person has to do some pretty fantastical mental gymnastics and tap dancing to reconcile the bible's stance on slavery with any kind of morality. That's why it's one of my first go-to examples. They clearly lay out that slaves are your property that you can pass down to your children, and that you can beat them as long as they don't die within a couple of days. It also instructs you where to buy your slaves (from the heathen that surround you) with different rules for Jewish slaves in that they're to go free in 7 years, but there's wiggle room in there so you can trick them into being yours forever.
It'd be one thing if the bible said nothing about slavery. Then you could just blame man, but it does, and in fact endorses it. Exodus 21, Leviticus 25:44, Ephesians 6:5, 1 Peter 2:18 and more. It's very clear. Like I said, I encourage anyone reading this conversation to check it out and decide for themselves.
I can understand your example of slavery as a justification for criticizing The Bible - it's the low-hanging fruit no-brainer argument. But, if you're expecting me to excuse or defend the passages related to slavery, you're swinging at thin air, because I won't.
Fundamentalists might look upon it as the infallible, literal word of God. But, as I stated before, I don't place Christianity above any faith - or non-faith, for that matter. So, I don't consider it to be the divine word of God. It is a work of its time, written by real, imperfect people, in the context of their era.
I don't consult The Bible for guidance on the acquisition of slaves any more than I do for the rules on what fabrics to wear or whether I can have lobster for supper.
Many arguments from atheists against The Bible are, in actuality, false dilemmas. You are presented with two options: either accept that everything in The Bible is literally true and factual (a position that is easy to attack) or, if you're not onboard with everything, you should dismiss it in its entirety.
My initial point - that 'chucking religion' would lead to greater cooperation and harmony is very unlikely - was not intended to start a theological debate. I still stand by that. The atheism vs deism argument is just a diversion.
As an aside, while the stereotype of the Trump supporter is a white evangelical, in the 2016 election, a significant proportion of Trump voters - 26% - were irreligious.