At least in Russia, yes. First in 17 century there was the Old believers schism (known as Raskol), which is in many ways similar to reformation-associated religious split in Western Europe, or at least was driven by similar social and historical forces. It is also different in many ways: essentially one may say that in Russia counter-reformation happened first, and reformation - later. First the state decided to unilaterally "update" the religious practices and customs, and only then up to 50% of population refused to follow these changes and stuck to the old ways. But pretty quickly the Old Believers movement acquired some similarities with the Protestant movements in the West: they were prosecuted, lost their priesthood (in some sects - temporarily, in some sects - forever, with a post-hoc theological interpretation of this change), developed something similar to the famed "protestant work ethics" (because otherwise they would not have survived the post-Peter double taxation), etc. They were also fundamentalists in many ways, so theologically it was a "rightist split", not a "leftist split" as in the West; and, again, it was not initiated by the Old Believers themselves, but still there are many parallels. We can talk more about it if you wish.

Then in 18 century Russia was overwhelmed with charismatic and mystic sects, known as Khlysty. They were severely persecuted (even more strongly than Old Believers), but in many ways they were very similar to Charismatic protestants in the West, just with a heavy Russian folk undercurrent.

And then the 19 century became ripe with what can be called "rational" sects, the biggest two of which were famous Doukhobors and Molokan. These appear to be directly influenced by Baptists and various sects popular among Volga Germans, but there was lots of convergent evolution with Quakers as well.

One can also say that a movement of anti-alcohol activists in the beginning of 20 century was heavily inspired by certain Protestant movements, even though "Trezvenniki" (literally: non-drinkers) never broke with the official church, but rather acted within it. For some reason I cannot find much information about them in English, so I'm not sure what to reference. Still it was yet another movement with a clear Western vibe (certain churches would be known as "Trezvennik" churches; they were a bit similar to the Salvation Armny in their attitude to the society, even if somewhat less intense)

Unfortunately most of these movements were either exterminated, or died out, or are close to extinction.

Edit: I can quote some sources in Russian, but I don't think they are translated, unfortunately. Let me know if you'd like me to dig the refs out.