You should be absolutely honest with your supervisor, and not lie about your feelings.
The same as if you were compelled to sit next to a Black, or a Jew, or anyone else you may not be able to tolerate.
Hopefully, they will be able to find you a place where you would be more comfortable. In any event, it’s really important that they know your feelings here, so they can take the appropriate action.
Certainly, if I was supervising an employee like you, I’d make sure your discomfort ended immediately, within the hour. I would also make a note on your HR file, so that future employers would be informed of your feelings.