There seems to be an opinion in the historical fields that there is a divide, or snobbery between Academic historians (those that hold university degrees), and “amateurs” who don’t, and are just enthusiastic.
Is there any evidence of this (e.g. a written paper)? I cannot seem to locate any sources from either side of this supposed argument.
A degree in any field, be it History or Astrophysics, carries with it a certain degree of credibility. Training in an advanced degree encompasses the fundamentals, critical thinking, and familiarity with the state of the field. The "State of the Field" includes the range of primary sources/precepts/data on any given topic, but also a handle on the (usually) centuries of secondary material which has been produced on that topic. Secondary scholarship is important because it builds on the collective "knowledge" of the field, each bit working with the other bits to form a sort of mosaic of accumulated progress. Academic publications is based on rigorous critique: for instance, in the case of Historians' articles in published journals, the submission goes through a double-blind gauntlet of review by colleagues. Article submissions which do not seem to have academic merit, or misunderstand source material, or present arguments based on erroneous assumption or bad science, do not get published. If I "self-publish" my academic article, I am bypassing that system. That automatically makes my paper weaker and less credible, no matter what brilliant insights I might have.
It is therefore ironic that you are asking for a "written paper" to tell you this. You are, instinctually, asking for an "academic" published voice to support the notion.
Is this system 100% fair? No. Academia is a closed loop, and you don't generally get to participate unless you buy in (literally!) and get an advanced degree. The major academic presses and journals will not generally publish a submission that does not have some kind of scholarly credential, though of course there are exceptions.
There are plenty of amateur historians out there who are energetic on this or that topic and know the ins and outs of that topic very well. Their opinions on that topic are not less valid because they do not have an advanced degree, but they are at an automatic disadvantage, especially if their views are at odds with the academic establishment.
I suppose I could place myself in the "amateur historian" category (Amusingly enough, with respect to /u/Alkibiades415 , I am writing a Master's Thesis in Astrophysics!) The field of my main interest is sufficiently obscure that you're unlikely to run into academics who are more familiar with it than me - essentially, they'll be a tiny subset of specialists in the Middle East and Central Asia (and many strictly speaking not "historians", but people with degrees in Religious Studies, Cultural Studies, etc, not that this matters much in practice). (Now, Classicists who think they know the subject is another matter...)
This is rather unlike more typical "history buff" subjects like World War II, US Civil War, Roman Empire, etc, where there are comparatively armies of big-H Historians for ever imaginable subset of the topics and their vast troves of primary and secondary sources. It's really hard to, as an amateur, even begin to get the kind of perspective that spending 10 hours a day for the duration of a PhD engaging with literature and perspectives, training your analysis skills, getting bad habits "beaten out of you" by supervisors critiqueing your assignments. In these subjects, I don't think it's really feasible to, as an amateur, really get to the point where you can compare to professionals.
Going back to my field of interest, where the amount of literature and primary sources are so much sparser, we should still consider what a professional historian, even one in a tangential specialty (say, someone specialized in Early Islamic Iran, Mongol Iran, etc), would have that I don't. They'd probably:
Be fluent readers of French, New Persian, and maybe German, giving access to a vast amount of secondary literature I can't read.
Have some proficiency in Middle Persian, or at least have had the opportunity to take courses in it.
Be far more trained in effective academic reading, that is, getting as much as possible out of a secondary work in as little time as possible.
Have the opportunity to engage with other experts on a daily basis.
And in the case of actual experts on pre-Islamic Iran, they'd very likely have some proficiency in Avestan, Old Persian, and perhaps Elamite, Akkadian, etc, giving them both access to and a grasp of primary sources that I, again, cannot even begin to compare to.
I could certainly put in the work to teach myself these languages, and I consider it from time to time, but that's such a big investment I find it hard to allocate the time and energy to even start to take it on. It's really hard to compete with someone whose job is to be an expert in a subject, no matter your "enthusiasm". And no matter what I do, I just don't have the possibility to go to academic conferences to schmooze have fruitful discussions with other experts - that's as important as anything else!
As I am fond of saying, there just aren't enough hours in a day.