Were there non-Scandinavian Germanic tribes that also raided and pillaged during the Viking Age?

I'm reluctant to call the Viking-Age societies of northern Europe 'tribal'. The word just doesn't seem to fit. I get the feeling that viking groups were pulled together through patronage and political affiliation (i.e. a jarl and his retainers, plus allies) or perhaps geography (i.e. a jarl and the free farmers or bondsmen from the fjord he dominated), rather than the putative ancestral origins that are often associated with the word 'tribal'. Scholars do refer to earlier Iron-Age leaders as chieftains and warlords, but they're increasingly referring to Viking-Age leaders as sea kings or pirates, depending upon how generous they're feeling.

This of course goes for the word 'Germanic' as well. Back in the 1800s, as modern historical studies came into being at the same time that the modern nation-state of Germany was beginning to come together, it was really important to emphasize the shared 'Germanic' history of all the little principalities from the old Holy Roman Empire that were getting pulled into the new Prussian-led state. Reference back to a proud Germanic past helped the German Republic that emerged after WWI endure revolution and the Great Depression, and of course this helped lay the groundwork for Nazi nationalism as well. In the wake of WWII, scholars have become skeptical of the utility of this 'Germanic' concept. As more than one scholar has noted, just because these people shared common linguistic roots doesn't mean that they shared anything else—genetic origins, cultural sensibilities, or political goals. And the Viking Age helps point this out. Scandinavians, although they all spoke a Germanic language, still managed to fight amongst themselves throughout the period, as the fledgling Scandinavian kingdoms consolidated and expanded, or fractured in intrigue and civil war.

Okay, these caveats aside, it's still very possible to answer your question with a definitive yes, non-Scandinavians were involved in raiding and pillaging during the Viking Age. Charlemagne and his descendants (who were Franks and therefore every bit as 'Germanic' as the Scandinavian Norse) were perhaps the most successful, ruthlessly raiding and pillaging from Spain to Saxony for over a hundred years. The English kingdoms accomplished the same on a more modest scale, with Mercia perhaps doing the best by using its central position to play one neighbor off the other until Norse warlords wiped the Mercian kingdom off the map. Further east, we have less definitive evidence, since these were not literary societies that celebrated their exploits in forms that survive today, but the chroniclers of Carolingian France admit that the tribes from modern Saxony, Prussia, and the Slavic Baltic states were particularly troublesome raiders, undermining their abilities to protect and keep allies in the region despite their periodic efforts to do so.

From an archaeological standpoint, we have a rare opportunity to know about the Norse raiding parties that came to Western Europe thanks to a unique site at Ridgeway in Dorset near the English Channel. A band of about fifty men, who appear to have been a viking ship's crew, were decapitated and buried in a sand pit on a hillside. Their bones don't show any definitive signs that they were captured in combat, but a couple heads are missing, which suggests that their capture and execution was at least prestigious enough to merit taking trophy heads.

Archaeologists have examined the proportions of certain isotopes in their bones, which contain signature traces of where a person may or may not have come from, as well as the food that they ate. These young men came from surprisingly diverse origins. Although many may have grown up in or around Norse Scandinavia, a number also likely came from Arctic and sub-Arctic areas of Scandinavia (perhaps Sami? Finns?), northern Iceland (so possibly with Irish grandparents), the Baltic States, Belarus and Russia. Moreover, the isotopes show that they all had very diverse diets and only started eating the same marine-rich diet about three years before their deaths, further evidence that this was a multi-ethnic crew. I, for one, am fascinated by the possibility that these men might have shared very little in common, perhaps even a common language, which makes it difficult to imagine how they would have been commanded and led into battle.

TLDR Yes, non-Scandinavians were involved in raiding and pillaging throughout the Viking Age. It was a cornerstone of political strength and masculine identity both in Scandinavia and abroad. And there's evidence to suggest that even some of the "Viking" raiders that showed up in Western Europe did in fact come from diverse backgrounds, so even the "Danes" of the textual sources might not all be Scandinavian in origin.