The prologue to The Fellowship of the Ring describes the Hobbits. Before The Shire was settled there were three races or types or ethnic groups or subdivisions of Hobbits: Harfoots, Stoors, and Fallohides, that later became quite mixed in The Shire.
The Harfoots were by far the most numerous and typical Hobbits:
the Harfoots were browner of skin, smaller, and shorter, and they were beardless and bootless; their hands and feet were neat and nimble,...
The descriptions of the Stoors and Fallohides do not mention if they had beards or how common facial hair might have been among them. At the moment I do not remember reading any mention of Hobbit facial hair.
I do not remember reading any mention of Elves having facial hair except in the chapter "The Grey Havens" in The Return of the King Cirdan the Shipwright is described:
Very tall he was, and his beard was long, and he was gray and old, save that his eyes were keen as stars;...
Tolkien also made an illustration in which one Elf is depicted either with a beard or with a dark shadow on his chin.
But Tolkien may have forgotten about that when he answered the question of how Legolas recognized that Prince Imrahil of Dol Amroth had part Elf ancestry.
At last they came to the Prince Imrahil and Legolas looked at him and bowed low; for he saw indeed that here was one who had elven-blood in his veins. 'Hail, lord!' he said. 'It is long since the people of Nimrodel left the woodlands of Lorien, and yet still one may see that not all sailed from Amroth's haven west over water.'
Tolkien once wrote that Legolas recognized Imrahil as part Elven because no Elves or part Elves have beards.
So why did he write that Cirdan had a beard?
Most of the ordinary Elves mentioned in LOTR might be only 457, or 1,519, or 2,821, years old when mentioned.
Cirdan was described in year 3021 of the Third Age. The Second Age lasted for 3441 years. The First Age ended 6,472 years before Cirdan was described as having a beard in TA 3021. Elrond was born 58 years before the end of the First Age, and so was 6,530 years old in TA 3021.
Tolkien wrote annals giving Galadriel's birth date in Years of the Trees, but unfortunately couldn't make up his mind if the Years of the Trees in Valinor were nine point something times as long as Years of the Sun, or ten times as long, or 144 times as long as Years of the Sun.
So Galadriel is millennia older than Elrond, but depending on the length of Years of the Trees, she could be 14.4 times as many millennia older. Nobody knows the relative ages of Cirdan and Celeborn. Cirdan was an important leader of the Elves far back in the Elder Days, ere ever Galadriel's father was born.
Celeborn is probably a youngster compared to Cirdan, no older than Galadriel, but might possibly be as old or older than Cirdan. Tolkien kept changing the backstory of Galadriel and Celeborn (including Celeborn's genealogy) trying to get it right, so nobody knows.
So Cirdan is probably the oldest Elf described in Tolkien's works, probably by thousands of years and possibly by tens of thousands. Some Tolkien scholars believe that Cirdan as the only described Elf old enough to grow a beard.