I should probably disclose up front that I’m not particularly interested in seeing the new Fantastic Beasts movie. I read and enjoyed the Harry Potter series when growing up like many my age but I know a lot of people that care a lot more about it than I do. (Playing real-life quidditch for six years will help with that.) But I do find one aspect of the many criticisms of this movie (see, e.g. this (spoiler-filled) article) fascinating: the continuity problems.
The question I’d like to step back and think about is: what specifically are the Fantastic Beasts movies in continuity with?
The most obvious problem is that the original Harry Potter movies and the books aren’t the same. While the books themselves are only in continuity with each other (unlike Arthur C. Clarke’s 2010: Odyssey Two, which is a sequel to the 2001 movie rather than the book), the movies are in a somewhat more complex state of being in loose continuity with both themselves and the books—I’ve seen criticisms that they are difficult to follow if one is not familiar with the source material. (A full discussion of their differences would likely be a full essay in and of itself, and frankly one that many other fans are more qualified to write.) The Harry Potter series is also notable for being one where the movie adaptations started coming out before the books finished, so a lot of readers’ interpretations of later books were necessarily skewed by movie interpretations of the earlier books. Most references in media to Harry Potter rely on the movies, as does the Orlando theme park.
Now, the flip side of arguing “movies are only in continuity with other movies” is J. K. Rowling’s statement that the movies are canonical because she’s writing them. While I’d argue that this is overly simplistic on its face (movies are inherently collaborative in ways that novels are not), the more interesting question is what weight we, as fans, should even place on this statement, and whether Harry Potter canon should even be considered open. Rowling has become notorious for dropping additional information that reinterprets the original novel series years after their publication. It is of course her right as the author to want Harry Potter to conform to her vision. But the reader has a right to what they get out of a novel’s text, too. Reacting to a book after you read it is just as valid as reacting to a story after reading the wiki and getting more information that wasn’t in the books. And it’s well-documented that an author’s intent can change post-publication: look at Fahrenheit 451, which Ray Bradbury described in 1956 as being primarily about censorship but later claimed that it was in fact a criticism of mass media.
And of course there’s the niggling little problem of defining the authoritative text of the books. I read the first American editions, which infamously make nontrivial and inconsistent changes to the British texts; the substitution of “Sorcerer’s Stone” for “Philosopher’s Stone” is the most prominent, but I will always have a special place in my heart for the Year 2 password to Dumbledore’s office changing from “lemon drop” in Chamber of Secrets to “sherbert lemon” in Goblet of Fire. The Harry Potter Lexicon lists the changes between the U.K. and U.S. editions and also mentions revisions made to the text in 2004 to fix continuity issues. Ultimately I’d think the “author’s preferred text” would be that found in revised British editions, which isn’t the text I’ve actually read.
The other and more insidious problem with allowing the powers that be to define the canon is that they have a financial incentive to tell you “yes, this is canon to the thing you love and therefore you must watch it”. There can be value in larger franchises in avoiding confusion as to what is and is not in continuity, but the only real risk of confusion here is where you stand as a fan. We’re not going to have a Great Assembly or Ecumenical Council of Fandom to decide what’s in and what’s out (and fandom needs no excuse to schism). If you’re having a conversation where the exact scope of continuity matters, it’s good to state your opinion upfront to avoid misunderstandings, but other than that, it’s your right to read and enjoy what you want.
Ultimately the original Harry Potter series told a story. It was a good story. It ended. The Fantastic Beasts movies are also telling a story. Whether or not you believe it to be another section of the Harry Potter canon or mere apocrypha is up to you.