In my opinion, the difference between a “fake fan” and a real one comes mostly down to how much *respect* they show the work in question, its other fans, and its creators. Fake fans will often nitpick a work’s flaws - no matter how minor - and demand very specific changes be made to it. Imagine, if you will, someone coming into your house and complaining about every aspect of the interior (or worse, mocking you for living in a house at all), then screaming obscenities and horrible accusations at you for daring to evict them. This is the Fake Fan, a cancerous tumor in a fandom who disguises itself as a “real” fan despite having no love for the work or its creators, nitpicking every minor thing, making up issues to complain about, and most annoyingly, demanding that changes be made to the work.
Naturally, this doesn’t mean a True Fan is supposed to ignore genuine problems with the work - for example, a game with tight controls having a sequel with floatier, less-responsive controls is a legitimate problem - but “true fans” will often critique objectively major problems, such as continuity errors or poor controls as stated above, and not minor or subjective issues such as representation - which is important, but not nearly as much as some make it out to be. Not all “real fans” are this wholesomely-minded, but as a general rule, fake fans will tend more towards “complaining” whilst real fans tend more towards “critiquing”; the difference being that one side genuinely wants to see the work improve for everyone, while the other wants to see the work improve only for themselves - or in some cases, doesn’t want the work to exist at all, seeing it as a blight on the world for merely existing - and the worst part of it all is: the fake fan will often call the real fan’s critiques the real complaining.
In short, the issue of real verses fake fan (in my humble opinion) comes down to how much respect they show the work, its fans, and its creators, or if they tend more towards complaining about the work’s minor flaws rather than its bigger, more subjective issues.