Mulan gave you good advice. As a former elder, and one who once had to counsel a brother about not wearing a beard, I know all the reasons. None of them are valid. What it really comes down to is this:
They say it gives the wrong impression in the field, that it makes you look like a rebel.
Hogwash! That may have been true back in the 50s or 60s, to some degree, but it is laughable today. When you have people in the highest levels of government, businessmen, educators, even Al don't-call-me-scruffy Gore wearing beards, the stigma is loooooong gone.
My advice, as an ex-elder, if they tell you to ditch the beard? Don't be confrontational, but gently question everything they say. If they tell you that it could cause a stir in the field, ask them how? If they say beards are not accepted in society, ask them how could that be when everyone can wear a beard nowadays and be fully accepted in society.
The elders have no leg to stand on in this case, other than hoping you will take the hint and comply. If you question them at every step, they will be stumped. Now, depending on your particular body of elders, and their personalities, this may royally piss them off. Proceed with caution accordingly, for you know them best.