Slytherincess makes the argument that the question is not subjective by linking to a "test" for the characteristics. There is no "official" test for this though, and even the test that she linked to seems very subjective. I'll highlight the cues that indicate that the results are subjective:
(0-16 Points) Most likely Not-Sue. Characters at this level could probably take a little spicing up without hurting them any. (17-21 Points) Fanfiction characters can go either way at this point depending on the writer. For an MMO/RPG or original fiction character, however, you're most likely perfectly fine. (22-29 Points) Original fiction and MMO/RPG characters can go either way at this point depending on the writer. Fanfiction characters may need some adjustment, however. (30-35 Points) Fanfiction authors beware - Mary's on the loose. There's still a chance you can save this character with some TLC, though. Role-players and original fiction writers, you should also consider tweaking your character. (36+ Points) Fanfiction authors, you might just want to start over. Role-players and original fiction authors, at this point your characters are likely to provoke eye-rolling and exclamations of "yeah, right!" from your readers. (Well, at least from me.) Immediate workover is probably in order. (50+ Points) It's probably a lost cause either way, or you didn't read instructions properly (some people don't [read this instructions], which causes freakishly high scores). If it's the latter case, read the instructions and take the test again.
Most likely, probably, can go either way, may need some adjustment, consider, might, likely. All of these are indications that the test itself is very subjective, so using it to declare the answer non-subjective is not accurate. The author of the test even addresses this by stating that high scores can be caused by just not reading the instructions carefully enough.
In addition to all of this, looking at some of the questions from the test, it is driven for use by the writer, not used to test someone else's characters. This is an important point because it makes some of the questions unknowable, and/or rediculously subjective. Examples of this are:
Is your character's name: A name you planned on giving one of your children?
Does your character look how you wish you look?
There are many more questions like that, and it is highly doubtful that JKR has discussed all of them enough for people to be able to answer them without some form of subjectivity.
Slytherincess also points out that
sometimes the characters one would least think of as a Mary Sue (Harry Potter) get the highest Sue scores, while characters who appear to be blatant Sues (Ginny Weasley) score much lower.
This is all evidence that the test, and the question itself is highly subjective. It is likely to garner a lot of debate, and will not have one correct answer. As such, it is not a good question for the site, and in my opinion should be closed (an opinion that the community agreed with).
Note: For those of you fixated on the fact that I said that the community agreed with the opinion originally, I apologize. I meant, that the community agreed with the opinion. I said "originally" to distinguish the fact that the community has since re-opened the question. It was meant to bring light the fact that the question indeed was closed at one point, something that may not be apparent to people looking at it now. I am fully aware that the community can't vote to re-open until it is closed, and did not mean to suggest that peoples opinions were swayed or changed or ??? whatever negative connotation that people were apparently attributing to the comment. It was only meant to distinguish the fact that A. The community down voted and closed the question, originally, while B. simultaneously showing that the community has since changed that decision.