Both phrases imply that they were at some point going to exist (the "yet" makes that explicit, even if it weren't implied otherwise). The difference actually has to do with what happened after they did come to exist.
The term "had existed" actually implies that something at one time existed but does not anymore. Likewise, "had not existed" implies that they had not yet come to exist, but then later they did exist, but then after that they ceased to exist again.
On the other hand, "did not exist" is more open-ended, it only says that they didn't exist at that particular time (but usually implies by context that they did exist at some other time). "Did not exist yet" clarifies this to mean that they did not exist at that time, but would come to exist later (but it does not put any end to that condition, so they could continue to exist now).
If "national skinheads" no longer exist now, then it would perhaps be technically correct to say "they had not existed yet", but this is a rare enough (and very specific) situation that the construct is almost never used, and therefore even in this case it would probably sound awkward to most listeners.