I read something recently that touches on this subject that I had never heard before. I've been reading the book 'Epidemics and Society' by Frank Snowden, and in the chapter about Tuberculosis, he comments that in the early 1900's it was commonly believed that going cleanshaven was a protection against contracting and spreading TB. Made me wonder if this could have been one of the reasons Rutherford was against beards.
Just a thought