short answer: fanfic can be critiqued.
longer answer: it's contextual, and there's a way to go about that I think 90% of present day fandom is incapable of.

longer-er answer:
by critique, I'm going to assume you mean based on the quality of the writing, story, and characterization, not trashing the fic because you just don't like it or hate the author or w/e.

the idea of "fanfic should not be critiqued because it's done out of passion and put online for free" is, at least in my experience, a newer fandom opinion. this is most evident in the difference in the "comment culture" between FF.net and Ao3. granted, FF.net comments had a tendency to become inflammatory ("NO FLAMING PLEASE!") but the point is that it was done.

hearken back to the days of LiveJournal and standalone archives, and you will see folks critiquing fanfiction like any literature. those archives were not like Ao3 where anyone with an account could post. oftentimes you had to prove to the community that your writing met their standards to be featured there. one could argue that the quality of the work was higher and therefore lent itself to criticism but then, you could make the same argument for any well-written fic. likewise, you took your fragile ego in your hands every time you posted to a LJ fic community because they had no problem exposing your flaws to you in the comments. that's not to mention entire communities dedicated to "sporking" what were considered bad fics. (fwiw, you'd also get ripped apart if the fic you were shitting on wasn't bad enough and it was obvious you just had an axe to grind.)

so in some ways, our interaction with fanfiction has improved and writers feel less anxious to post their work even if it's not polished. however, critique is a part of discussion. if one is asked, "do you like this fic?" and their answer is "no", they should be free to express why so long as they do so respectfully. yes, fics are (usually) written out of love for the canon and published for free, but so are a lot of things that are openly critiqued. webcomics, for example, are passion projects published for free. it has also become increasingly common for fics to be pulled offline, given a bath, have a few names changed, and then published professionally. are they now open for criticism? even though they were once written for fun and for free? are they not essentially the same works with the same characters?

that said, I don't think the average fandom member knows how to thoughtfully critique a piece of literature. for one, people in fandom often have a hard time separating their personal preference from their judgement of a fic on the merits of the story alone. that is to say, someone claiming a fic they otherwise enjoyed is garbage because the wrong guy bottomed is, while a valid reason to no longer read it, not exactly a fair criticism of the work itself. furthermore, I don't think it's necessary or appropriate for every fic published. does someone's 3k word smut fic clearly written one-handed need to be analyzed with a scholarly eye? no. should we be pointing out every SPaG error on a child's first fic? absolutely not. but a highly regarded multi-chapter work that is often recommended and discussed? if done correctly, I don't see the harm in writing an honest review. there's plenty of fanfiction that is just as good as any book, that's why the medium has become so popular, so it makes sense that people would want to approach it the same way.

do I think people should start leaving such thoughts in comments on Ao3? no, I do think those should be for spreading positivity. I also don't think it should be done directly at the author unless requested. but if someone wants to write a blog post giving their opinion on a popular fic in their fandom, again, there's no malice in it. unless there is in which case yeah, fuck that guy.

me personally, I don't want my shit critiqued because my skin is thin layers of ice barely hanging on, but I don't think I'm above it. I also don't think I've published anything worth critiquing.

(also I know I'm a hypocrite because I've responded to questions with that answer before- passion projects made for free yadda yadda- but it was in response to someone asking if I thought any fics were overrated I believe, which is a question never asked in good faith haha. at the end of the day, I do think that should be kept in mind by both readers and writers. don't judge yourself too harshly. easier said than done.)

(Teddy is my kyman next gen if you guys aren't aware, and CC is kz's creek next gen and they're in luv)

ohhh good quastion ummm

Teddy would say ✨EVERYTHING✨ but his favorite things about CC are her resilience, although he doesn't think she should have to endure anything unpleasant, and her humor, even if she uses it to antagonize him. and her big hairy bus--

and he'd probably describe some huge sweeping romantic gesture here, but I think his actual favorite thing to do with her is have one of their lazy days at home watching movies or playing games in their sweats, eating junk food, and then sharing a home cooked meal at the end of the night. which is ALSO very romantic, I'd say.

ahaha I think you're asking the wrong guy but uh scratches head

okay, so some of the hottest bottom Kyle I've ever read is hidden on the kink meme. afaik Anon hasn't uploaded this anywhere else:
https://south-park-kink-meme.dreamwidth.org/445.html?thread=78525#cmt78525 (mob/Kyle)

when I say this reads like it was written in one feverish sitting, I mean it in the best way because the frantic energy of the writing matches the tone of this piece so perfectly it should be studied.

Tentacles? Tentacles by Rainbow_Convection
https://archiveofourown.org/works/50706469 (Kenny (Mysterion)/Kyle)

Rainbow fics are always a banger and this one has tentacles if you can believe it!! just great monsterfucking plain and simple

might last a day (minus forever) by cherryvanilla
https://archiveofourown.org/works/420889 (Cartman/Kyle with past Stan/Kyle)

this is an older fic (in the grand scheme of things) and technically they switch in it BUT it's definitely that vintage mountain kyman/bratty Kyle that I find people look for when they want bottom Kyle forward fics. there's scenes from this I've never been able to get out of my head and the smut is top shelf imo.

here's a kyman rec list I made a while ago that has a mix of top and bottom Kyle although it's top heavy because I worship at the temple of bottom Cartman. see, it's not about Kyle for me.
https://retrospring.net/@shortkingkenny/a/111293811561394631

and you should check out my friend Sam kyman4lyfe because she writes a lot of bottom Kyle and in fact just posted something where Kyle gets a bunch of holes filled by a bunch of guys:
https://archiveofourown.org/users/kyman4lyfe

and here's her curiouscat because she can help you with this question so much better than I can:
https://curiouscat.live/kyman4lyfe

sorry I couldn't be more helpful! I'll post these links on twitter too.

I think he'd be a better dad than people expect him to be. he's still Cartman though, and he falls into the trap of wanting a built-in best friend that his own mother fell into with him, but at least in my heart and soul he's got a partner to rein him in. in lieu or terrorizing his classmates, he acts out a lot of his maniacal schemes on the PTA, which he has been kicked out of several times but still shows up to every meeting.

he also likes to play the "good cop" to his kids. reprimanding falls on his partner, that way he can be like "oh well, that was your dad's idea :/" later.

overall though I think he's a lovable papa bear who means well, despite being who he is. he has to be. for my personal id.

hi sammmmm!!!

my ideal kyman date for them? I'm pretty simple. I like them going out for a nice meal, something they've planned for in advance. Kyle's hopeful heart is out of step with his logical mind. he tells himself tonight will be different. they'll go out, eat, have a few glasses of wine maybe, go home and have sex, brush their teeth and go to bed.

but that never happens because he's dating Cartman and Cartman always finds a way to turn a simple dinner into a catastrophe. they have a loud argument at the table (Kyle gets hard about it) or Cartman organizes some elaborate and obnoxious romantic gesture (Kyle does not get hard about it) which turns into a loud argument at the table (Kyle DOES get hard about it). OR Cartman starts having a loud argument with the couple at the table beside them because they told him to shut the fuck up, and Kyle jumps in because nobody yells at his man except for him (Kyle gets hard about it).

so they drive home, and Kyle's got this begrudging boner the whole time and Cartman's like, "wasn't that great, babe? why don't we do that more often?" while Kyle's white knuckling the steering wheel.

then they have really insane sex involving props. they don't go to bed until like 3 because Cartman insists they doordash something after. Kyle forgets to brush his teeth, wakes up three hours later for work still pissed off and horny.