Both modern studies found no impact on the efficacy of oxygen masks. One was done up to 25000 feet, the other at 30000.
SFU STUDY BUSTS MYTH ABOUT FACIAL HAIR ON PILOTS - Faculty of Science - Simon Fraser University
Analyzing the air mask fit for bearded commercial airline pilots.
The FAA document from the late 80's cites research from the 70's, which mostly seems to cite research either by the US Air Force even earlier (that was possibly biased), or by respirator studies, which are not the same as crew oxygen supply.
It would be interesting to know what literature the consultants reviewed as all recent literature points towards beards not being an issue.