How can we help religious people better understand & accept science?
Please discuss in comments.
I feel that one major issue we face is a fundamental gap in epistemic foundations.
Non-believers almost universally demand empirical evidence for claims, while the very idea seems to be rejected out-of-hand by many (perhaps most) theists (when it isn't taken as an act of personal persecution). Others assert that various objects from the lowly banana to "everything" are brimming with said evidence - and ponder profusely as to why the atheists don't/can't see it.
The evidence by design has been, I think, throughly trounced by the scientific establishment by now. We know, with mathematical precision, how a myriad of simple mathematical models can yield an appearance of design without any actual design being present, it simply emerges from the mathematics. The Mandelbrot fractal is a good example of this, how breathtakingly beautiful and literally infinite complexity from such a simple equation, and there are an infinity of such equations. We know the KINDS of chemical arrangements that must have come about for abiogenesis to have occurred (and progress is made almost weekly on the open questions with absolutely no hint that there is an actual problem with organic life having arisen naturally). We understand VAST amounts about genetics and have a deep knowledge of exactly what types of genetic alterations actually occur to explain the evolutionary process (the idea that macro evolution is impossible is patently absurd in the face of modern evidence, present in hundreds of thousands of scientific papers and many thousands of books).
At the time of Darwin writing the Origin of Species (a book a HIGHLY recommend you tackle - librivox has a free audiobook version) his arguments were circumstantial - he repeatedly and profusely confesses the limitations of his evidence at the time and gives numerous cases which present difficulty. What is amazing is that he came to his conclusions with only knowledge of basic inheritance - he had absolutely NO knowledge of what we today call genetics: DNA, genes, mutations, etc. One might be excused in the early 20th century of rejecting the claims as lacking sufficient evidence - but today, such evidence is as incontrovertible as the ontology of the Earth's gravity. It certainly can be denied, but you would look rather silly tumbling down a cliff-face.
Atheists do not grant theistic presumption, we don't have to 'disprove' your god, any more than we must disprove Ereshkigal. This line of argument is often dismissed by theists but I suggest you look into this question much more deeply.
Why are the claims about YHWH valid while the claims about Ereshkigal are presumed to be false? I know that you have accepted the version of god you happen to believe in, primarily by accident of birth, to be the one true god - but does that version of god REALLY align with whichever Holy text you happen to accept as truth (be it the Torah, the Bible, or the Qur'an or whatever)?
Usually not, most people end up having to excuse the actions of their god as "mysterious" which strikes me as avoiding cognitive dissonance from an honest reading of (e.g.,) the bible.
Science doesn't claim to have all the answers, that seems to be the major objection to it from some quarters -- but to pretend to have answers, many of which are ultimately harmful to human society, seems to me to be the greater absurdity.