From the error, it sounds like an issue with your includes - I would double-check that before troubleshooting anything else. Theoretically, if you are using Objective-C++, you should be able to include C++ headers just fine.
Though from a brief search, I did find references that "sometimes this can lead to issues", without any specific cause mentioned. From what I've found, it suggests exporting a C interface and using that in your Objective-C program. To do that, you would need to isolate all your use of Eigen to a C++ translation unit, write your own C wrapper around it, using something like
#ifdef __cplusplus
extern "C" {
#endif
// Your wrapper implementation here.
#ifdef __cplusplus
}
#endif
You would then need to build your wrapper with a C++ compiler. Once you have that, your Objective-C program should be able to link to this without issue.
~Antonio