I like to think that Elves could grow beards, if they wanted them, as it might throw up all kinds of slightly uncomfortable* hormonal problems otherwise! Maybe it was the Elves' culture to prefer to be clean-shaven, and Numenorean Men followed them in this 'fashion statement'. As to why Cirdan grew a beard, maybe it was the influence of living out on a limb from most other Elves, or he kinda liked the style statements made by them Istari when they arrived on the shores of Middle-earth?
Mind, I always picture Elrond with a beard - and I'm not the only one, as Alan Lee does, too.
*Literally...