Modern religion (or modern theism in general) is not based in logic. Science is. Therefore the two will never find a way to prove each other right or wrong. It is just impossible. Unfortunately it doesn't end there. For many of us here would conclude that having logical thinking is they way to go (and I agree) but we can not expect to ever reach a point where this disagreement will ever be settled. Personally I feel this is where religion looses its ground. Not on the fact that religion may always have another reason to believe, despite the mounting scientific evidence to the contrary, but rather on how religion has been redefined since the last scriptures were written down. The characters of the bible where always basing their belief in evidence. Miracles, unlikely military victories, etc. Although I don't believe that the two will ever be 100% compatible or agreeable, the religion of that time may have had a lot more in common with the scientific method of today.
In case you have not seen this movie (Nacho Libre), this isn't just a meme, it is a real line from the movie.
With that said, we always run the risk of simply falling under the religious mentality. That is that you know better because you have your Almighty God in your side, whom knows everything and is capable of anything. Religion defined as worshipping of a deity is the default understanding of it. The reality is that we can make a religion out of anything. If the WT every said anything correctly is that patriotism for example, can be a form of religion. No, I do not advocate for not saluting your flag or any of that. But in the fervor of national pride we loose sight of the real purpose of why we classify ourselves under a book of laws, national name or flag or anthem. This is to care for one another and provide a level of equality and governance. We eventually turn patriotic fervor to the point where it becomes just as unreasonable as modern religion. We make the constitution our bible and we attach ourselves to it and listen to no reasoning and all our very own selfish purposes. One has to simply look at the battle over the second amendment in the US to see a clear example. Regardless on which side of this debate you seat, it is not difficult to see that some are too quick to resort to the constitution as an irrevocable basis for their stand. Any non believer would probably agree that even if the bible has some good advice, it was written thousands of years ago and therefore outdated to modern life. Yet, a book that was written a bit over 200 years ago, in an age where no one could have imagined what a modern weapon could do, seems to hold up to modern times and therefore worthy of outmost consideration.
The key in all of this, in my view, is wether we are making our life outlook or belief into a religion worth fighting for and worth proven ourselves right rather than imagining how our life outlook can help our fellow man without causing any further harm. Science has a leg up on this for sure and by far. At least in modern times.