Purists are those fans who prefer an item to remain true to its essence and free from diluting influences. In media, a fan would prefer the original form of a work over remakes or adaptations.
In Tolkien fandom, fans who are characterized as purists, have a more serious and “strict” view on Tolkien's legendarium. Most Purists are Tolkienists and therefore the term may be meant to connote more sophisticated appreciation, in contrast to the casual, junior "fanboy". On the other hand, the term can be derogatory as it can imply elitism.
Purists are generally indifferent to fanon and fan fiction or even dislike it. Deviations, alterations, cuts or additions in derivative works, are deemed unnecessary or even offensive, especially if they are not compatible to the wishes or spirit of Tolkien.
A purist would notice, find and criticize elements in an adaptation of Tolkien's work, which is not found or deviates from the original. A purist would also try to dispel misconceptions that have stemmed out of the adaptations, fan fiction or misinterpretation of Tolkien's writing.
Such a phenomenon was seen as a reaction to the movies by Peter Jackson. In that regard, purists have been contrasted with "revisionists" who accept and respect the changes in the grounds of artistic license.