We'll need to examine a few different aspects of this context to understand fully.
Please note that I'm going to frame this around theism and not religion, since religion is shooting fish in a barrel, in terms of contradictions with science. I'm more interested in addressing the basic idea of believing in a god without any extra baggage, whether you're Christian, Muslim or Whateverian.
If God is Real
The only way science and God would be compatible is if God were real, and science would determine so. We don't have any indication of that yet, but beyond that, we're not really talking about whether a god is real, but whether a belief in a god is compatible with science - just so we're clear on the scope of this discussion.
Superficial Context of the Discussion
|Ferrofluid with magnet below|
(GNU licence on image)
The problem I see with theists claiming the answer "no", is that they couch the answer with a trivial point. They may say something like:
My belief in God has nothing to say about the existence of ferrofluids or semiconductors, which are science topics. Therefore, science and theism are compatible.Sure, you can just pick some obscure science topic and see theism not have anything to say about it. This approach to answering the question is basically cherry picking. What we need to examine is the implications and broader scope.
What Effect does the God have on Reality?
I wish I still had the screen capture, but I apparently lost it. My sister popped into Facebook stating something to the effect of:
Why couldn't Evolution be true and God just play some role in it?She's suggesting "theistic evolution" basically, which is an attempt to have both science and theism playing well together.
Science is necessarily sacrificed. Why? Science would reveal that all the mechanisms of Evolution, and even the precursor to Evolution - Abiogenesis - occurred under natural circumstances and events. To suggest that a god played a role is to contradict science - is to replace something science would determine, and inject a god in its stead.
In a theist's world view, for every point in which they believe God plays a role in reality, if the science contradicts it, their belief in a god trumps the science.
In this way, they are mutually exclusive.
The only reason why they have any regard to science at all is either because the particular topic of science isn't important to their theism, they decided to side with science over theism (for instance, that evolution is true and creationism isn't), or they decided to side with theism over science (for instance, God started life and abiogenesis didn't).
Their world view is a heterogeneous mixture of mutually exclusive chunks, between science and theism. The only god that can be even mildly compatible is one that has no influence on this reality at all (deism).
Skepticism (Or Scepticism for those Europeans who spell it wrong)Skepticism is at the core of science. It literally couldn't function without it.
Skepticism is the process of doubting claims until they're sufficiently justified. You'll see this in the peer review process, studies, etc. Theism is not skeptical - unless they actually do have sufficient evidence to justify the claim (which, for many definitions of God is impossible by definition).
In order to believe in a God, one must abandon skepticism, and thus, a scientific mindset. Again, theism and science are mutually exclusive.
Atheism and TheismThe difference between atheism and theism is that the atheists decided that skepticism/science was more important, whereas theists abandoned skepticism/science to maintain their belief.
Theism - A Shadow of it Former Self
Modern day non-fundamentalist theists aren't aware of how much ground they've lost. A few thousand years ago, their theism laid claim to the topics of disease, the origins of lightning, reproduction, cosmology, earthquakes, etc.
Year after year, century after century, at each step that science has investigated (though it was informally "science" before Francis Bacon did his thing), each one was determined to be merely another natural mechanism. When the evidence became overwhelming, the majority of theists accepted that disease was caused by germs and viruses, instead of being possessed by demons.
The modern day typical theist is a result of theism giving way to science on topic after topic. Their god has very few places to hide anymore, in what few gaps of knowledge science has left (at least in terms of the readily observable phenomenon).
On each point, the people had to choose whether they'd accept science, or continue believing their theistic assertions, and on each point, science has been winning.