I can speak to the US, UK, Germany and Greece, all of whom have active movements at present — with England’s two groups currently the most activist and noticeable. Although in Greece, the degree of stress and the Greek problem of Turkish immigration into Europe (akin to Mexican in the states) is the fuel for an rapidly expanding movement.
The fascist (Nazi) movements consist largely of working class males. In these countries, the movements generally expand during times of economic duress. This is because of a variety of factors but largely that these males are displaced by competition from immigrants. (There is some suspicion but not good data, that it is driven by difficulties in finding mates as well, since mates are a status symbol.) Their concern in this regard is not without merit, really. In their view, they tow the social line, adhere to rules and norms, and are not rewarded for it, and instead are displaced both economically and socially. So they see society as ‘unfair’ to them.
These movements are not large. In the single digits of suport. (Although in the UK they have managed to capture of few seats recently. But because these movements are vocal and somewhat frightening, they get a lot of press. Consequently, the governments tend to be highly concerned about them. In no small part because they are subgroups of a supposedly social majority that is not satisfied with the state of affairs, thus invalidating the existing government, and posing a threat to the dominant political ideology. It’s probably useful to keep in mind that a) chaos and loss of faith in a government can occur more easily in a country than we assume b) a revolution only requires that five to ten percent of a population be united and willing to deploy violence in some organized fashion. So it is not irrational to take these groups seriously if they have any chance of getting above five percent support of the population.
But in real terms they are not so much politically influential as they are a measure of dissatisfaction that is so great that it is driving some percentage of the population to advocate violent change to the status quo. Their very presence is a meaningful yardstick.