The Moslems have those who adhere to Sharia, the Jews have the the ultra-orthodox, and the Christians have the Pentecostals, etc. And if these examples aren’t representative, then pick a more appropriate example. But, each major religion has adherants who follow the letter of their own particular laws. And in many cases, they are missionaries, as well. But is there a way to assess the relative percentages of these major religions that one would call fundamentalist? Our press would have us believe, I think, that virtually all Moslems, for example, are extremists and fundamentalists. Clearly, this is not the case. But what, exactly, IS the case? Any way of knowing?
You could spend a liftime of gathering data and making guestimates and still not have anything more the an educated guess.
No way to KNOW!
Why not? Are you saying it is impossible to do surveys of religious belief?
I have no idea what the answer would be to the OP’s question, but I fail to see why finding out is completely out of the question.
from OP
“But what, exactly, IS the case? Any way of knowing?”
You’ll never know exactly! A reasonably good guestimate maybe.
This is not a simple question.
For starters, how do you define “fundamentalist”? Do you have to believe in Creationism? Do you have to belong to one of the more conservative sects (like Southern Baptists) or is it possible for an Episcopalian or a Unitarian to be a fundamentalist? And where do you draw the line between a fudamentalist and a person who is simply a devout practitioner of their faith? Or is everyone who takes their faith seriously a fundamentalist?
I’m not trying to be argumentative; the term “fundamentalist” is very vague. And whatever definition you come up with, other people will be using a different one. For example, someone who burns down an abortion clinic is most certainly not following Jesus’ teachings, but many people would call him a “fundie.”
I’m aware of the difficulty of defining “fundamentalism.” Typically, however, at least in Christianity, it refers to someone who adheres to a literal reading of the text. In Islam, I believe there are those who do the same with reference to the Koran. (They memorize and attempt to follow it in its 7th century, or so, version). In Judiaism, again, there are those who read and follow Torah literally. If one uses this, or any other related definition, which religion has the highest percentage of fundamentalists?
I respect that you’re trying to get at a real issue but the definitional problem really is hopeless. Given different contexts, histories, theologies, etc you’re juggling way too many apples an oranges. For example Christian Fundamentalism is primarily a U.S. Protestant movement - should you include very conservative Catholics? Should you talk about the percentage of Protestants that are fundamentalist or the percentage of Christians as a whole? Are pentacostals really fundamentalists? Not really. Most importantly are Christian Fundamentalists really reasonably comparable to Muslim or Jewish “fundamentalists?” I could go on. But the more you think about it the more bogged down you get.
There’s been a sort of working definition of fundamantalism, I think, in the headlines for the last several years. It might be phrased, “supporting extreme violence to achieve religious goals”. Perhaps it is somewhat of a misappropriation of the “fundamentalist” classification, but if this working definition interests the OP (or if it now interests anyone), there’s an answerable and important question here.
The context of this working definition has been comparison of Christian and Moslem extremism, for example comparing Moslem attacks such as September 11 and Israeli restaurant bombings and other Middle Eastern attacks with abortion clinic bombings by self-identified fundamentalist Christians.
This strikes me as a step toward making the claim that similarly small fractions of Christians and Moslems endorse such violence. Some of the articles I’ve read explicitly state that only a tiny fraction of Moslems support the anti-Western terrorism we’ve seen so much more about lately, more or less like only a tiny fraction of Christians want to bomb abortion clinics. These articles equate fundamentalism with supporting violence.
However, the admittedly infrequent polls of the Arab street that I’ve come across in the press paint a different story. In answer to questions like “Do you support the methods of Osama bin Laden” or "Do you want to see Americans killed? or “Do you believe God approves of the killing of Americans”, in places like Palestine and Pakistan, 50% to 90% answer yes. Somewhere around here I have a short list of the polls I came across (not sure where it is now).
Of course, some polls of the Arab street find that most Arabs believe, for instance, that all the American presidents have been Jews. I remember seeing one where a substantial minority stated they believed the American president is a disguized winged lizard, or something similarly bizarre, which might say more about how literally the statements were meant to be taken - I don’t know enough about it to make sense of that one. Polls I can remember chose their subjects by where they were found, not by their stated religions, so we wind up mixing “Arab” and “Moslem” as categories. But in the places the polls were taken, that probably doesn’t introduce a large error.
Ok, how about if we narrow down the definition to those who are actively working to make the world a place where everyone is a ______. Fill in the blank with Jew, Christian or Muslim. Maybe not an advocate of violence toward that end, but a willingness to accept it if one must. THAT type of fundamentalist. Then what would the percentages be? (actually, I don’t think any Jews consider that a goal, although I know some Christians and Muslims do.)
You’re correct. If I’m wrong, someone Jewish should come in and embarrass me, but Judaism lacks that evangelical strain.
And not to hijack things too much, but why is Judaism the third major religion? There are WAY more Hindus (around 800 million) and Buddhists (more than 300 million) out there, and more Sikhs as well. I think what you mean is “the Western religions” or “the major Western religions” or something to that effect.
A possibly less useful but easier question to answer might be to ask what percentage believe their particular holy work to be literally true and inerrant.
Handy rule of thumb: completely disregard any article which makes reference to the buzzword “Arab street.”
When I taught English in the Gulf, students did ask me if Abraham Lincoln was Jewish, because his name was Abraham and he had a beard. Reasonable enough. Most of my students thought that something like 1/3-1/2 of America was Jewish, that being the only conceivable reason we’d be such supporters of Israel, which isn’t entirely unreasonable from their experience. Yes, the society was highly anti-Jewish paranoid, but the supernatural didn’t enter into it.
Most of my students also thought the US was about 1/2 black, owing to TV, sports, films, etc. Again, not nuts in context.
Most Muslims do literally believe in djinn (“genies”), which are mentioned in the same lines as men and angels in the Quran. But then a majority of Americans, in contrast to just about every other Western nation, literally believes in angels. Some of these djinn are depicted as leathery-winged types, and the ones in Oman turn you into a donkey. A little weird? Sure. But surely no stranger than “Touched by an Angel.” I never heard anyone suggest American presidents were djinn. For one thing, they’d be depicted as being a whole lot more clever. 
I think the OP is asking a perfectly reasonable Q based in literal belief of religious texts. I think it is possible to make assessments on the % of each “major” religion (I’d drop Judaism from the list and add Hinduism if you’re defining ‘major’ as posting big numbers wordlwide… switch that back for the US alone) if you set up some consistent criteria about literal as opposed to symbolic belief and meaning of supernatural events in holy texts. Numbers for sect membership are certainly out there once you do that.