Can you provide an example?
There is this “Interview with a Montheistic Pagan”, this page talks about monotheistic paganism, and I have been told more than once that The Church and School of Wicca considers itself to be monotheistic.
It was no longer dominant but it did survive, despite persecutions, a few Naodisurvived to pass on their traditions, so it never had to be reinvented as with Wiccan rituals.
Because they call themselves pagan doesn’t mean that’s the meaning.
At least some dictionaries give that as the definition.
Merriam Webster:
I think this is the right answer. We can name plenty of elements of modern culture that come from pagan European practices, but these came to us through Christianized peoples who retained some of their ancestors’ pagan practices but who themselves had become Christian.
Obvious examples:
Halloween, based on the Gaelic harvest festival of Samhain
Yule logs at Christmastime, based on the Norse holiday of Yule
The days of the week in English, based on a combination of Germanic and Roman gods
The days of the week in Spanish, based mostly on Roman gods
The name of the holiday of Easter, based on the Germanic god Ostara (most other European languages use the Hebrew name for Passover instead)
Easter eggs, based on imagery associated with the Germanic god Ostara
Various expressions/idioms, such as “By Jove”
Various other terminology, such as calling “thunder” after the name of Thor
Lots of traditional fantasy imagery, such as witches, wizards, fairies, banshees, etc., based on old deities or (in the case of witches and wizards) former pagan clergy (not Wiccan, but superficially similar)
I’m aware of that. But I think to meet the OP’s criteria, the naoides and their followers/adherents would need to be people who rejected Christianity and did not identify as Christian, rather than people who combined Christianity with observation of traditional Sami practices or adherence to traditional Sami beliefs. And (SFAIK) we’re not aware of any people meeting these criteria in the later 18th century or beyond.
[…of a pagan but monotheistic religion.]
Well, one modern-day one would be Pastafarianism.
The critical problem with this (and perhaps with the OP) is that it is difficult to identify a specific point in time when a people truly change religion. Social change is often gradual and subtle. Also consider that various peoples were (and are) influenced by neighboring religions even without large scale (or even any) conversions, meaning that nobody’s practices are “pure” of outside influences. For example, post-Vatican II Catholicism adopted a more Protestant-style Mass ceremony without actually becoming Protestant per se. Whether a specific change represents heresy or simply another way of doing something or thinking about something is impossible to define scientifically and is subject to the opinions of religious scholars.
Also, how do you handle crypto-converts who nominally “convert” to a dominant religion to gain social status but continue to believe in the old faith? Do these people become non-(old religion) followers as soon as they undergo a nominal conversion, or do they only truly convert if and when they develop true belief in the new faith? What about a historical figure like Julian the Apostate who was raised by Christian converts as a Christian from birth but who converted to his grandparents’ religion in adulthood? Was there a true “break” in his family that made Julian’s paganism a reconstruction, or was it still possible for him to convert to the true, old paganism?
Some forms of Hinduism are monotheistic.
I think everything you say is correct. We tend to think of a religion as being like a church; not just a set of beliefs and practices but an institution with a formal structure, a visible presence and an identifiable membership, and if you’re a member of this institution then you’re not a member of that institution. Indeed very often, in the forms of religion that we are most familiar with, these institutions define themselves in opposition to one another. (E.g. Protestants are so called because they protest against Catholic beliefs or practices.)
But in fact most religion, historically, hasn’t been like this, and even Christianity hasn’t been. While there are core Christian beliefs that are original to Christianity, a large part of the corpus of Christian beliefs was inherited from Judaism or taken on board from Greek or later influences. And the corpus of Christian practices is even more diverse in its origins.
So paganism-with-Christianity versus paganism-instead-of-Christianity is probably not a very meaningful distinction. What you have is Christian adherents who retain extra-Christian beliefs, values or practices, and then the church decides if that’s permissible or not. And if it’s not, and people are forced to choose, they have creative ways of refusing to choose (e.g. crypto-paganism, or stubborn adherence to syncretic practices) or any choice they do make might be provisional (they’ll conform, but at a later date, or from time to time, resume the forbidden practices).
What you don’t have is pagan institutions analogous to churches, parishes, dioceses, etc surviving alongside and in opposition to Christianity. But that’s because most of the pagan traditions never had institutions of this kind in the first place. In so far as there was, say, a "church’ of the Norse religion it was simply the community, observing Norse beliefs and practices collectively. Once the Norse communities are Christianised, you now have a community that combines the Christian and Norse religions in various ways (though usually with the Christian religious traditions front and centre and Norse traditions at the margins). What you don’t have is any community of people following the Norse religion unaffected by, and in opposition to, Christianity.
What about the Khanate of the Golden Horde? The retained some heavy non-Abrahamic beliefs until pretty late.
I’m unable to “quote quotes” (if it’s indeed possible to do); but anyway – referring to all in dropzone’s post #10. I recall reading a comment, telling of a situation as in quite recent decades, by the parish priest of a remote rural Irish community: his words were in affection and regretful resignation, rather than vehement anger or despair. He described most of his parishioners as holding, simultaneously, several apparently incompatible points of view. To wit: that of standard Catholicism; the view that this world and this life are all that there is, with any spiritual dimension to life not being real; and belief, to quite some extent, in the ancient pre-Christian spiritual / supposedly “mythical” stuff.
Yeah, I must admit, this type of conversion would be difficult to trace. You can’t measure something that a person is motivated to hide, in fear of pain and death. Fear of persecution by the Christian majority must have kept a lot of people at least nominally compliant!
Most of the discussion here has been Euro-centric, or least in the context of Western culture. I guess it’s a natural consequence of using a word (“pagan*”) derived from Latin, and used in context of a Latinized Christian church discussing non-Christians in their awareness.
But Shinto is Japan’s polytheistic religious system with continuous recorded practice since before the 8th Century CE. Ainu shamanism may be as old or perhaps older than that.
*From the Latin “paganus”, “one who lives outside the civilized areas.”
Personally, I think it’s a natural consequence of the OP specifically asking about Europe. But I could be wrong.
Still, there’s lots of pre-Christian syncretic stuff still around- Yule trees, Christmas hams (both Yule-related), Christ depicted as Helios, etc… A lot of it is just considered “Christian”, since it was syncretized so early on that it’s now tradition- e.g. Christmas as Saturnalia, the celebration of Christ’s death and resurrection happening at the same time as all the pagan vernal equinox fertility festivals, etc…
I hadn’t considered Shintoism or shamanism. Good examples!
My initial intention was to limit the instances of pagan holdovers to Europe, but why not broaden the scope? We can go global if we like! Fascinating discussion…
OK, so what you’re looking for is more of a map of current distribution of religion. There are large swathes of Asia, Oceania and Africa where the religions of the Book are minorities, recent arrivals or both. China and India, for example. Tribal religions are present in much of the Americas, although in many cases there has been sincretism in multiple directions. Do you count candomblé and its cousins voodoo and santería as “traditional” or not?
Fight the [del]power[/del] hypothetical! 
Yes, it would be neat if we could take a magic time telescope and peer into the brains of ninth century Irish people and say, “This guy is a true believer in Catholicism, this other guy goes to Mass as a social thing but really believes in the all old gods and secretly attends a crypto-druid service in a basement on alternate Tuesdays when the Catholic priest is out of town, this guy in the corner doesn’t know what to believe, and this fourth one is a monotheist, but his god is Brigit according to what his grandma, a descendant of the founder of a fourth-century Druid reform movement, taught him in secret…”
This sort of phenomenon can also be seen in non-religious contexts much more recently. The Appalachian Mountains in the USA have preserved some 18th century Scottish practices (especially as it relates to music) that aren’t what you are going to see if you land in Glasgow tomorrow and walk around town.