So... I don't remember if it is established but I feel it's implied and basically an unstated fact that Crowley and Aziraphale's bodies don't require human functionalities such as the need to use a lavatory, sweat or age. - Any change in their appearance is intentionally made and manifested by their will or as a reflection of their emotional state (they can still feel sensations and discomfort etc.)
Basically, their appearance doesn't experience any change unless they want it to Hair doesn't grow or develop, and they don't age- they don't accumulate dirt or get dirty unless outside factors affect them (soot from a burning car/bookshop - Paintball stains and flying birthday cake etc.). They do not even need to shower or bathe. (Although I think Aziraphale still would because of the whole, 'I'd still know it was there... underneath' thing and just the whole indulgence of the activity would delight him)
Having established these conditions I now ask you this -
What exactly does Aziraphale even do when he visits his barber?
We know Aziraphale is a creature of comfort and habit. He very rarely changes his appearance and latches on to the things he likes. His hair we know doesn't exhibit change throughout the centuries - he mostly goes for a change in facial hair style in favour of the times fashion.
My theory is that Aziraphale visits his barber annually (or perhaps semi-annually) at the same time and on the same day.
As part of his little ritual, I posit that he "miracles" his hair to grow 2 inches in length the very morning of his appointments to see his Barber only to get the length cut back to its usual state - exactly.
Do I think Aziraphale on the appointed days also allows a miracle of scruff on his chin for a shave? Personally... No- I feel like Aziraphale would have a sensory issue / discomfort with the sensation of a dusting of small hairs groaning out of his face. But I do imagine he'd find the process of a professional shave quite relaxing and luxurious.
- Therefore I think he'd miracle a full fluffy beard just to have the satisfaction of having it lathered and shaved of again nice and smooth.
AND THEREFORE BEARD-ZERAPHALE MUST BE REAL!!!
Does he need to go to the barber? No? Does he experience the physical changes that would require a barber? Not unless he manifests them intentionally. Is it purely for self-indulgence? The relaxing routine experience of a haircut, a manicure, and a shave? Absolutely.