I've found the problem. FBX file format was set to FBX 2016 at the export default preset, I changed it to 2014 and Maya Toolset started to work with fbx again. Sorry for bothering you, I should search better before writing here. However, there is still a minor bug: Maya Toolset won't bake fbx (with the same error I mentioned before) until I open and close Maya's export window, even with fbx export plugin checked.