As a believer/follower of Islam, I believe in the oneness of Allah and in His being free of any deficiency. With that, I believe that His knowledge is absolute/perfect while ours isn’t. He knows many things that we might never know. Having said that, I’m not sure what you mean by dilemmas arising from science and religion, but the first example that comes to mind is that not too long ago, people would say that red wine is beneficial using science as a basis. Now, being a Muslim, just because it supposedly had some basis in science, this would not push me to consume it as it went against what my religion told me. Similarly there is the case of pork, which even scientifically they said was harmful due to them not knowing how to cook it properly to kill any harmful microorganisms in it but now they can. Though this may be what they say using science as a basis, I will still not consider consuming it.
I will stick by “pure” (Islamic) religious beliefs even over what may be “proven” by science. I also believe that Islam doesn’t need to be revised. This goes back to my initial point and belief that Allah is all knowing and knows what we may never find out. He already knows what will be beneficial to us and what won’t. However, there is a framework to derive rulings that might not have been addressed at the time of its initial establishment, and many times to derive rulings, scientific knowledge is leveraged.