Speaking as an American of Irish descent, I wear a short mohawk whenever I'm off duty, and I've done a bit of research into the background.

We know a pretty good deal about the huge variety of hair styles worn by Gaulish, Germanic, and Briton tribes. Both from tools they left behind and Roman descriptions of them. It's unlikely that one possible example can change that.

Neither the Celts nor the Vikings had one specific hairstyle. This too was based on the tribe itself mostly. In Vikings the salves had their hair short and the others had medium to long hair. The tribe that Pliny speaks of apparently the men bleach their hair more than the women.

The Gaulish tribes reddened their hair and of course the Germans close to this area. One carving, in a Normqan grave, shows an almost goatee style of beard with a really short bowl cut on top of head. Some statue carvings show bangs, others not. Some with waxed look pointed mustache ends curved upwards. A bronze head of odin also shows this. Many vikings in fact have full moustaches and clean shaven chins. For Viking women, they seemed to favour the blonde hair. The women servants also wore short hair. Some say the married women wore a cap over their locks and had to wear their hair up in a knot.

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Celtic Hair was long according to Caesar and a few other sources by the free classes and for both men and women.

Warriors, on the other hand - (Roman sculpture of the 'dying Gaul' and the soldier from the Book of Kells), have hair that looks like a bowl cut, higher at back and longer over the eyes. The cut is much like the 'glib' style worn by soldiers in late medieval Ireland. Warrior soldiers and lower-class men wore a long moustache without an accompanying beard. One of the tests for membership for joining some of the elite warrior groups was that the candidate had to run through a wood, chased by the entire Fianna, without having a braid of his hair loosened by the branches.

Sometimes, on the occasion, they wore their hair in a multiple elaborate curls and braids they decorated feathers, gold balls, silver and bronze ribbons, thin flexible gold plates, or gold balls and other ornaments fastened in their hair. In the Tain Bo Culaigne, a beautiful woman wears three braids of hair wound round her head, and the fourth hanging down her back to her ankles. One of the tests for membership into Warrior class was that the candidate had to run through a wood, chased by the entire Warrior band, without having a braid of his hair loosened by the branches.

Diodorus of Sicily - says the Celts were tall and muscular, with pale skin and blond hair which they highlight artificially by washing it in lime-water. They then gather it back from the forehead to the top of the head and down to the nape of the neck... and therefore the hair becomes so heavy and coarse that it looks like the mane of horses. Could be they considered the Unicorn or Horse God as their Mother.

Irish texts refer to hair so long and stiff that it would have impaled a falling apple. The Irish hero god CuChulainn is described this way, and it is added that his hair was of three colours, darkest near the scalp and lightest at the end. If he is a Hound constellation we can see the dimmer stars, or it could be the reference to the style of bleaching they learned to do.

I highly recommend checking out The World of the Celts by Simon James. It's an excellent introduction to Celtic culture through an archaeological/anthropological angle.

Regardless, criticizing the practice as 'cultural appropriation' is a silly argument. Cultures all around the world have worn Mohawk variations. Whether it's the most thought of Pawnee, Mohawk, and Iroquois, or the lesser known Cossacks and Mongols. Using Native American religious face paint patterns would be disrespectful, cutting your hair in a globally common pattern isn't.

Sources:

1. Ancient Celtic Hair Styles and Decoration - Copyright 2010, LaurieLee Mills August 4th, 2010) (blog)

2. Celtic Hairstyles, Grooming, and Hair decor (blog)

EDIT: Added second source