Precisely. As an aside on that, anti-Semitic Muslim terrorist groups have cultivated links with European and US neo-Nazi groups, including skinhead groups in the "black metal" and other genres.
My understanding of the shaved head thing is that it was an outgrowth of British Mod/Rocker fashion differences:
Skinheads, named after their shaven heads, are members of a subculture that originated in Britain in the 1960s. Skinheads were closely tied to the Rude boy of the West Indies and the Mods of the UK.
SNIP
London in the early 1960s was experiencing a growing class separation between the working class - struggling, relegated to substandard housing, and increasingly neglected by their political representatives - and the middle class. Those youths who could afford it invested in new fashions popularized by The Beatles (haircuts) and Carnaby Street merchants (clothing). These were the Mods, a youth subculture noted for its consumerism and affection for style, music and scooters. Those of lesser means, such as the dock workers, made do with the practical styles that suited their employment - steel-toed boots, straight-legged denim jeans, and shirts and braces (suspenders in the US) often handed down by their fathers. When possible, their limited funds were spent on smart outfits worn in the evenings to the dancehalls, where they danced to ska, reggae, and rocksteady beats alongside their Jamaican coworkers.
Around 1965 a group of "hard" or "gang" mods, who could be identified by their shorter hair and working-class image, emerged from the larger mod scene. This resulted in a schism that produced "peacock mods" (The Who, The Kinks) and skinheads, commonly known by that name by around 1968. (Other early nicknames included "lemons", "peanuts" and "suits.") Early followers were mainly interested in and influenced by Jamaican Reggae and Ska music (aka, The Spirit of 69), Jamaican Rude Boy culture and a dislike of those perceived as the 'ruling classes'. They had an extreme dislike for the government and many larger businesses as both appeared to lack sympathy for the increasingly desperate straits of the working class.
Skinhead culture exploded in the year 1969, to the extent that even the rock band Slade adopted the look, after which the original skinheads slowly dropped into new categories, including the "Suede-head" (defined by the ability to manipulate one's hair with a comb) and the next-stage "Smoothies" (often with hairstyles down to shoulder length). Fashions within both groups regressed to their mod roots, reintroducing the common wearing of brogues (originally an identifier once boots became too conspicuous) as well as the slacks-and-sweater look. Here was a far cry from the singularly blue-jeaned and typically steel-toe booted skins of the past.
During the mid-1970s in the UK, the skinhead movement was reborn in an unexpected way. With the introduction of Punk Rock to the public, kids were looking for the next great shock-rockers. Skinheads with shorter hair, less emphasis on style, and a new sound grew in numbers and grabbed the attention of the media as a result of repeated incidents of hooliganism during football matches, often to the point of rioting between rival groups of supporters. Whether these riots were, in fact, initiated by skinheads or by overzealous fans in general is the subject of some controversy, but it is clear that skinheads were eager participants.