Sure you can use it with GPL'd software[0] or MIT licensed software! It doesn't stop the GPL from applying to any GPL'd code, nor the MIT license to any MIT'd code. The AGPL does say that when it is used, the sources must be available to the users; but that doesn't mean that when someone takes your (MIT or GPL) code and changes it, and uses it [without MuJS or other AGPL code], that the AGPL applies.
[0]: GPLv3, that is. Fortunately, most GPL stuff is "v2, or at your option, any later version." Unfortunately, there is quite a bit of just v2 stuff out there.
AGPL code can be dynamically linked to GPLv3 code. That's about the extent of their compability. Statically linking MuJS in even a GPLv3-licensed program would be a violation of at least one or the other, and virtually all other cases of linking - dynamic or static - with AGPL code would also be a violation of at least the AGPL (and possibly the other license, depending on its terms).
So yeah, sure, you can incorprate MuJS in an MIT-licensed project, but by doing so, you're effectively required to license the entire work (your code + MuJS) under the AGPL (or a license - like the GPLv3 - that's explicitly authorized for dynamic linking; this, again, doesn't apply for static linking).
[0]: GPLv3, that is. Fortunately, most GPL stuff is "v2, or at your option, any later version." Unfortunately, there is quite a bit of just v2 stuff out there.