It looks like traditio is against beards on altar servers and priests. At my chapel one of the servers has a beard. And there are SSPX priests and resistance priests with beards. Traditio would not approve.
From traditio:
A Reader Asks: "Is It Traditionally Permitted
For Altar Servers to Wear Beards at the Altar?"
From: Leo
Beaded Eastern Priest
A Bearded Schismatic Eastern Orthodox Priest
The Romans Condemned Beards as an Effeminate Practice of the East
Roman Priests Are Traditionally Prohibited from Wearing Beards
Following St. Peter, Who Shaved His Beard when He Became Christian
As It Is Considered Prideful in a Priest to Draw Attention to Himself
The Same Practice Should Be Followed, as Far as Possible
By Laymen Who Serve at the Altar, Most Particularly Young Laymen
Dear TRADITIO Fathers:
I am writing to ask you whether it is traditionally permitted for altar servers to wear beards at the altar. I don't remember any of the servers wearing beards in the past, but this practice seems to be becoming more common in Novus Ordo churches.
The TRADITIO Fathers Reply.
The Third Council of Carthage (397) forbade clerics to wear long hair or beards ("nec comam nutriat, nec barbam)" because a shaven face is one of the accepted external signs of the clerical state and is part of the habitus ecclesiasticus of clerics in the Roman Church, as well as being the Roman custom from ancient times into Christian times: "non nutriendi capillos nec in genis nec in mento."
Roman priests are traditionally prohibited from wearing beards, as it is considered prideful in a priest, who is thereby drawing attention to himself, whereas the attention should be paid to Our Lord. The Romans were meticulously clean shaven until the time of the ɧoɱosɛҳųαƖ emperor Hadrian (r. 117-138), who adopted unRoman practices. The Romans considered facial hair effeminate and a trait of the effete East.
The Jєωs who did not convert to Christianity retained their beards, as the Orthodox Jєωs do to this day. The Council of Limoge (1031) held that St. Peter shaved his beard when he became Christian, so his successor priests were expected to follow suit.
Beards in Roman practice are considered prideful; the humble man shaves. The principle is the same for women: woman's uncovered hair in Church is considered prideful and exhibitionistic. That is why St. Paul enunciates the Christian principle: "But every woman praying or prophesying with her head not covered disgraceth her head" (1 Corinthians 11:5/DRV). In Islam, beards are viewed as an "adornment," and Mohammedan men are encouraged to wear them to honor the infidel Prophet Mohammed.
For priests in particular, beards constitute practical problems of sacrilege. When Particles of the Most Blessed Sacrament or of the Most Precious Blood fall into a beard or moustache, how does one practically clean out the Particles or Droplets? If one has ever seen the Sacred Host fall onto the floor by accident and remembers how vigorously the priest attempted to clean out the Most Blessed Sacrament, sometimes cutting out parts of the carpet to burn, one understands why the Roman Catholic Church does not permit beards on its priests.
Only limited exceptions were ever permitted to this traditional Roman practice, but the basic principle remains the rule. "Exceptio probat regulam." One sees many violations of Roman Catholic tradition and practice in the Newchurch of the New Order, a fact that is not surprising, as Newchurch is not the Roman Catholic Church. The same Roman traditional practice should be followed, as far as possible, by laymen who serve at the altar, most particularly young laymen.
http://www.traditio.com/comment/com1612.htm