According to https://github.com/kripken/emscripten/wiki/OpenGL-support the support is stable for features that are directly available in WebGL and OpenGL-ES-2. Legacy, fixed function pipeline OpenGL code is not yet fully supported.
I suggest you rewrite your program to follow modern OpenGL principles, i.e. don't use built in matrices, use generic vertex attributes, vertex buffer objects, use shaders (vertex and fragment); within the featureset providede OpenGL-ES-2.