Several Inhumans fans disliked how Marvel was trying to push the Inhumans to become popular at the expense of the Mutants and wanted to have both species stand side-by-side. Others were just grateful that the property was actually getting major recognition at all from Marvel.
As of late, the decision to write the characters out of the comics and largely ignore them in most media has become this. While few would argue that the Inhumans being pushed to replace the X-Men wasn't handled very poorly, there are those that feel it's the right call given how toxic the brand has become, while others think it's going too far in the other direction and ignoring the property's stronger aspects. This especially intensified in the wake of Ms. Marvel (2022), which changed the MCU's version of Kamala Khan from an Inhuman into a mutant.
It's Popular, Now It Sucks!: More like "It's Being Forcibly Dragged Into The Mainstream, Now It Sucks". Inhumans had long been regarded as one of the Marvel Universe's hidden gems, but when the characters were forced into a greater presence in the setting, some of that appeal had diminished. A lot of it, of course, had a lot to do with how they were dragged into the mainstream, and at the expense of Mutants at that. Many have noted that the Inhumans being a Suspiciously Similar Substitute for the X-Men is very tin-eared noting that its overall set-up, i.e. a Hidden Elf Village with Crystal Spires and Togas has more in common with say, Asgard, Wakanda, or the Fourth World (to cite some of Jack Kirby's creations which scholars see Inhumans as containing a dry-run of), than a largely urban teenage-centric superhero group who live in contemporary society, and the overall eugenicist based self-exclusion from humanity has nothing in common with the X-Men.
Overshadowed by Controversy: Because 20th Century Fox had the film rights to X-Men and Marvel CEO Ike Perlmutter did not want to give prominence to a franchise that was making money for another company, for most of the 2010s he pushed Marvel to downplay the prominence of the X-Men and mutants in general in favour of pushing Inhumans as the standin for oppressed minorities. This reached the point that the Inhumanity storyline created a shedload of new Inhumans in an event which also directly horribly killed the majority of mutants. Since X-Men had for decades been orders of magnitude more popular than Inhumans ever was, and mutants had always been an allegory for racial and sexual minorities while Inhumans not infrequently represented isolationism and intolerance, the backlash was swift and vicious. Even after Disney's acquisition of 20th Century Fox led to mutants being restored to their original prominence while most of the Inhumans have either died, been depowered, or left the planet, it's impossible to discuss them without somebody bringing up the Character Shilling of the 2010s.
Replacement Scrappy: While they were pretty popular before, and individual Inhumans are still quite popular (e.g. Kamala Khan, the current Ms. Marvel), this is what most of the fans saw them as after Marvel tried to push them as a replacement for Mutants.
For the Comics:
Broken Base: The post-Infinity era, headed by Charles Soule. Either it was a new golden age for the franchise, bringing them into the mainstream and giving them the attention they deserve or an Audience-Alienating Era that was removing much of what makes the Inhumans unique and making them the poor man's X-Men, complete with the overexposure.
The Inhumans' status as social outcasts is largely self-imposed, as they possessed both advanced technology and superpowers well back into ancient times when ordinary humans would not have had the means to persecute a society that had either, much less both. They practice eugenics and maintained a sub-race of deformed, genetically engineered slaves called the Alpha Primitives. Their internal culture is a mess of a caste system (a fact which Maximus has exploited more than once) despite their comparatively small population. Plus, the current "heroic" royal family overthrew the previous monarch because they did not want to give up the Slave Engine, a device intended to transform humanity into Alpha Primitives! At best, their "heroism" is analogous to the characters of A Song of Ice and Fire (or its adaptation Game of Thrones). Even their status as Mutant analogues is dubious, since the majority of their mutations are activated deliberately via Terrigenesis, and if they were to forego the desire for superhuman powers they could still be Badass Normal types like Karnak even without it, whereas mutation is random and the Mutants live in a dominantly-human society where they have often been subject to persecution! Any Body Horror or Power Incontinence actually are their faults because, unlike Mutants, they get to choose to play the Superpower Lottery. Though much of their "less-than-stellar" aspects have been retconed, destroyed with the crashing of Old Attilan, or dissolved as part of Character Development. Especially their Fantastic Caste System and abolition of Alpha Primitives.
It's even worse in the case of the NuHumans who will often undergo Terrigenesis without even being given a choice in the matter. All in the name of making Inhumans more like mutants.
The Inhumans vs X-Men running plot, particularly Cyclops' involvement in it - namely, he was painted as mutant Hitler for destroying one Terrigen cloud (which, lest it be forgotten, sterilised or killed all Mutants it came into contact with) and then standing up to Black Bolt, before being vaporised. While it transpired that he'd already been dead long before any of this took place, having died of M-Pox from the cloud, and everything that followed was Emma Frost manipulating events with her powers to give him a martyr's death as part of her progressive Sanity Slippage, very few people actually knew that, and Black Bolt still vaporised what he thought was Cyclops. Of course, considering Cyclops' popularity as a Well-Intentioned Extremist rebel, it could have been a meta move on Marvel's part.
During Inhumans vs. X-Men, even a number of Inhumans admitted that the X-Men have a lot of very real bones to pick with the Inhumans, and narrative sympathy is definitely weighted towards the X-Men.
With fans of the X-Men. Originally the two didn't mind each other, but after a massive marketing push by Marvel billing the Inhumans as "the next big thing!", the two seemingly can't stand each other. This stems from the Inhumans going from their own unique thing to being Suspiciously Similar Substitutes for the entire mutant race, which many feel was because of Marvel not owning the film rights to the X-Men.
Following Inhumans vs. X-Men, it's got better, thanks to Medusa finding out just why the mutants have been driven to a last ditch attack (the Terrigen cloud is about to dissipate and infect the entire planet, rendering it uninhabitable for mutants), and deciding that Terrigenesis, sacred as it is, isn't worth the death of even one mutant, let alone all of them, destroying the remaining cloud. With that, the rebounding of the X-Men in ResurrXion, and the Inhuman Royals heading back off into space to find a replacement for Terrigen, meaning that the two groups are no longer in competition, relations have cooled significantly.
For that matter, "classic" Inhumans fans and "modern" Inhumans fans, mostly coming from the older fans who think the new breed destroyed the concept in the name of pandering to a nonexistent fanbase, and the newer ones who think the old Inhumans comics were an embarrassing relic that nobody really cared about. This is only exemplified by the Death of the Inhumans storyline with the main controversy being how the push into mainstream had destroyed the brand.
Genius Bonus: "Terrigen" is likely taken from "teratogenesis", literally meaning "monster birth". This is a Fridge Brilliance if it's intentional.
A subdued version of this can be seen again with Crystal and Ronan the Accuser.
Even Janet Pym called out Crystal and Johnny's relationship when Crystal called out Janet for wanting to wed the mysterious new Yellow Jacket from an old Avengers comic.
Tearjerker: The romance between Gorgon's daughter and Reyno, an Alpha Primitive child. Since she's the daughter of one of the royal family, she can't really be seen with him, and Gorgon's forcing her to go through terrigenesis (such a great father), which is changing her physically and mentally each time. The two run away to the Fantastic Four for help... and Reed refuses to do anything for fear of upsetting the Inhumans. So poor Alecto is taken back to Attilan and made to go through with the process anyway. Some time after, the boy tries approaching Alecto, only for her to harshly yell at the primitive daring to speak to her... only for her to suddenly break out crying, because she just can't keep up the pretence, and she still loves him.
Unintentionally Unsympathetic: The push into the mainstream, meant to garner new fans, soured a lot of people either because it came at the expense of the X-Men and mutants at large by bringing them to the brink of extinction with near-universal hatred again or because of the general mayhem and chaos of a lot of people's lives being ruined from being mutated, some to death. A lot of it is directed at Black Bolt, for unilaterally causing it in the first place after the last time him blowing up a terrigen bomb nearly screwed over the universe, with some spilling over to the royal family for being rather self-possessed in addressing it. There's a prior storyline in the Mighty Avengers where a king is deposed, replaced, and erased from history while given a lot of sympathetic traits, such as respect for their slave race, and the reason he was deposed being his decision to disable/remove the Slave Engine, an Inhuman gene-altering weapon created to mutate regular humans into more Alpha Primitive slaves, something that the other Inhumans denounced him for. The fact that they're quietly retconning Black Bolt into being megalomaniacal and the royal family into being more noble is rather transparent.
What the Hell, Costuming Department?: Some of Maximus's costumes over the years have been... kind of goofy. Especially the green and black outfit with the oversized ruff.
The Woobie: Many fans feel sorry for Luna simply due to the fact that she has Crystal and Quicksilver as parents. She’s suffered a good amount because of their respective selfish tendencies.
