It is the many assumptions that are accepted in most religions that are the problem.
It's not a problem, it just isn't scientific. Philosophy is not scientific either, but there are many avenues where science can be applied.
A crude example would be the angels-dancing-on-a-pin religious question that some well-meaning people tried to apply the scientific method to once upon a time
I have never heard of this before so I looked it up. All I can find on it seems to be a philosophical exercise and not any scientific endeavor. Do you have information on it outside of that?
Unfortunately, there are at least two assumptions that must be made before that question can be looked at scientifically: the existence of pins and the existence of angels. (There are many more, such as the motivation for divine pin dancing in the first place, but this is just a crude example anyway.) One can devise an experiment to demonstrate acceptable pin-ness of a given object, but there we have to stop. One cannot build science on unsupported (by science) assumptions.
Like I said, all I can find on it is philosophical concentration- and modern usages to somewhat denote the same as naval gazing. Are you one of those people who suffer this spokism or whatever in that you simply cannot fathom philosophy without passing it through a scientific lens?
This sort of thing happens at every level of religion. That is why science tends to be incompatible with most of them.
Not at all. The vast majority of religions is little more than historical accounting's with meaning pressed into them.
At the most basic level, there should be an experiment such that if I do X and Zeus exists, then A should happen, and if Zeus does not exist, then B should happen.
Is there an experiment you can conduct to see if my friend Frank exists like this (oh yeah, without gaining his explicit permission or demanding his attendance)? Does that mean Frank doesn't exist or he is incompatible with science? You are talking about an experiment to compel someone or something with a free will to do something specific in order to satisfy your curiosity. Try going hunting sometime. You can get all the calls in the world, spray yourself down with animal piss, spend shit loads of money on clothing that masks the human scent, and still sit in the woods all damn day without ever seeing the game you are after. That doesn't mean it isn't in the woods or even those woods, it just means they didn't pass by you. This happens all the time to some hunters and even nature watchers. You simply cannot force something with a free will to jump and that doesn't make it incomparable with science either. Think of free will as being a choice of when two mixture are combined, to either change color or not at it's choosing.
Science can't disprove many aspects of most religions and that is why it's incompatible. The devil is in the assumptions, you might say
Science cannot disprove many aspects of reality either. You cannot scientifically disprove the other guy ran the red light which caused the accident most of the time. You cannot scientifically disprove my friend Frank exists. You cannot disprove my accounting of something that happened in third grade when I was the only witness. What you can do is say there is not enough evidence. But more importantly, even without being able to disprove any of that, you can scientifically address aspects of the crash from the running of the red light, you can scientifically address things Frank has done, you can scientifically explain whatever I claims to have witnessed in third grade, therefore just like religion, it is not incompatible with science. There are just areas that reach outside of science.