Yes the Navy allow beards - but only proper ones, not goatees. However, moustaches are strictly verboten in the Senior Service - so where is the logic?
I would suggest that you get rid of it when you go for interview then grow it back once you get the job (although they may complain!). Sure, it is probably unfair prejudice but as Bill Gates once said "life isn't fair - get used to it!".
It is also worth noting that goatee beards (or those that just encircle the mouth) have the unfortunate effect of making you mouth look like female gentitalia- Just a thought!