Het or "gen" vs. Slash Fic. This war often has a hugely homophobic subtext, with defenders of het or gen claiming that Slash Fic must be centrally about sex, that it's disgusting, that it's offensive in some way or another whereas their own is absolute canon. In fact, the homophobic subtext is so common that issuing one of the more generally seen as homophobic criticisms of slash will often get you seen as a troll or raging bigot or both, even if somehow you did intend to "only discuss fanfiction and not real GLBTQ people" - which is often seen as a "Just Joking" Justification in and of itself, because of its frequent use by actual homophobes and trolls.
Any fansite devoted to One Piece will burn to the ground if someone says the forbidden word: Zolo.
Want to see mushroom clouds erupt all over the area? Go to a Daria fan board and type in the following words: "I like Tom Sloane."
Cupcakes. Sweet Celestia. The conflict this story has raised among Bronies is enough to make Nightmare Moon shudder.
The Conversion Bureau. Mention this on FimFiction and watch explosions blossom all over the place. To put it simply, half of the comments on these stories decry the series as disturbingly misanthropic and riddled with Unfortunate Implications, while the other half fanatically defend it as an accurate representation of humanity's flawed nature.
Generally, trying to engage truly serious issues (or serious issues that are usually treated as cheap angst or the like with the seriousness they deserve) or explore unusual kinks, unless you are writing for a private audience that has been informed of what they are about to read, is a bad idea to do in Fan Fic unless you like being a controversial figure and the central point of many flame wars.
Unusual kinks, even if they are canonical, are a frequent source of Flame War, because unless the fic is kept very private or is anonymous and no one recognizes your style, people who don't have those kinks (and sometimes, regarding canonical ones, aren't even familiar with the canon) will both assume that you're writing the fic as personal masturbation fodder (as opposed to, say, exploring the characters or writing outside of one's comfort zone, which are some major reasons for writing unusual kink fic) and that you're trying to make "your" kink "normal" or being intentionally offensive. Especially expect to be flamed if the kink's potential appeal isn't easily understood or if it involves furries.
Detailing that Inferred Holocaust as an actual apocalypse or genocide? You will catch flames for upsetting people, possibly even from appointed fandom Moral Guardians if the fandom had a canon rating below PG-13, and flames if you held back on the gorn at any point, allowed a Karma Houdini or hated character to survive, broke up a beloved ship or turned a Happily Ever After future into a Crapsack World or a beloved character into Hitler 2.0, and for writing dark and depressing shit that isn't canon.
Implying the Happily Ever After pairing became an Awful Wedded Life or broke up in a nasty divorce will earn tons of flames, never mind that the Real Life divorce rate is around 50%, even for originally happy couples. And if it broke up for another ship, Ship-to-Ship Combat will at least be invoked, and if said ship is a slash ship, just... go live in a bomb shelter for a bit, as that's nuclear flame war.
Writing something like alcoholism or drug use or Self Harm as it really is as opposed to being a cheap source of hurt/comfort or humor? Cue people who only know it from fanfics and who never met a real alcoholic or drug user/never did the research you did/never had the experiences you did telling you how wrong you are and how depressing the story is and how it can be really, really cured by true love/by religion/by Epiphany Therapy and why is it such a big thing for the character. Or, alternately, Moral Guardians accusing you of glorifying it or wallowing in it. Or alternately, people with actual problems being offended that you dare write this stuff and assuming that you must, yourself, have a problem and need to go to therapy rather than write fanfiction. Worse, watch as fics that actually dangerously depict or trivialize such behavior don't get flames, and do get "awww, poor baby, sex will fix him." Trying for a balanced story by showing the drug user/self harmer to get some good out of the "bad" thing? Again, nuclear flamewar, as you will be seen as glamorizing and trivializing even if your point is that just because some good feelings can happen during something, that doesn't make it good.
Depicting lolicon or shotacon for the purpose of deconstructing it and showing it as the child abuse that it is? Again, cue a nuclear-level flamewar, as you'll first have to deal with the people who read the early part of the story, get triggered or otherwise enraged, and announce you to be a pedophile and that they don't need to read any more to know what vile filth the story is and you are, and that they are immediately reporting you to law enforcement. Once you get past them, then the next up are the people that will be absolutely enraged that you are taking their pedo porn fantasies and crushing them into the ground because OMG, why is the little boy/girl emotionally and physically traumatized and why is their romantic hero being hauled off in handcuffs by the police? And finally, if you've made it to the end without having to explain yourself to law enforcement or whatever else you're reported to as a result of the first group, and haven't Rage Quit after going into an Unstoppable Rage at the second group, there will be the people who will flame for the story being out of character or depressing in general, as above.