the compatibility issue

Is science compatible with religion? It's a very popular question currently, not only directly but in an indirect way, with so many believers of an intellectual persuasion employing scientific techniques, or at least the language associated with them, to render their beliefs more persuasive to themselves and others. It's surely a great compliment to science that so many modern believers feel the need to invoke it in the interest of their beliefs - though it should be noted that this tendency hasn't spread to Islam to any significant degree. Though there are obviously only two possible answers to my initial question, there are two opposed perspective from which each of these two answers can be given. The two answers are of course yes and no, and the two perspectives are the religious and the scientific. From these we arrive at four possible positions:

[1] religious compatibilism - this is the official position of most of the established Christian churches, though whether it is tenable is another matter. There's also the question of whether this compatibilism is sincere, or an alliance of convenience with an untamable adversary.
[2] religious incompatibilism - the least interesting position intellectually, but also by far the most popular, given that the vast majority of the human population know nothing or very little about science, and of that majority almost all of them are religious and take their religion very seriously.
[3] scientific compatibilism - a position taken by some scientists, who claim that science and religion operate in mutually exclusive spheres, so that they can do their stuff harmoniously, presumably by completely ignoring each other. [Most, and perhaps by definition all, religious scientists are compatibilists, due to the primacy of their religious beliefs].
[4] scientific incompatibilism - to my mind, the only coherent position.