Crabb, 43, was the first Tory Cabinet with a beard when he was appointed Welsh Secretary in 2014, the group says.
They added that Crabb's promotion following the resignation of the "follicly challenged" Iain Duncan Smith has "increased the profile" of beard wearers in national politics.
The group's spokesman Keith Flett said: "Of course the first principle any Minister with a beard will have in mind is ‘no cuts’".
But questions are already being raised about how long Crabb can maintain his facial hair.
And he's been accused of "hipster entryism".