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.)