"Most atheists have a Protestant inheritance". Thank you, as I had my own suspicion this be the case but didn't find any compelling evidence to support this assertion. Do you have any such evidence?
As far as I can tell, the only aspect of "reality" that could justify the use of the term "determinism", is in the fact that "reality" is "determined" to constantly change. It's possible there might be some form of "reality" without any change but as far as I can ascertain there isn't any evidence of anything that doesn't change. However, there is no correlation of the cause and effect principle with this "deterministic" change, as the effect can become the cause for the original cause and then diverge later into another effect. Can the heat and light become a tree again? Yes, but this constant flow of change has nothing to do with "determinism" outside of that "deterministic" change. There is however, I believe, a pattern of [Reason] within "reality" that isn't "random" but has a characteristic tendency to change according to that pattern but then this is also divorced from direct relationship with the cause and effect principle.
I'm reading my own words and I imagine it won't be clear to the reader. Best I can do is to use the tired analogy of coin toss, where the [Reason] would be the probabilistic outcome of 50/50 heads vs tails but the [Reason](probability in this case) isn't part of the cause and effect for any individual coin toss.