Hmmm, difficult. One of these sets off my troll vibe and the other one doesn't. However, one was posted by a new user while the other was posted a known and respected user of the community. I can't be sure that this doesn't influence me.
I can objectively see a difference in the presentation. Both questions present flimsy clues, but what they do with them is different. The Major Nelson qeuestion asks the question in a neutral tone. The Dr McCoy question is more of a case of “your answer is provided along with the question” and “it is a rant disguised as a question” — some of our signs of questions not to ask (it starts with “There is plenty of evidence to conclude”!).
So far the Dr McCoy has had several flags in addition to the visible close votes. The Major Nelson question has a single close vote.
I don't see anything intrinsically wrong with asking about a character's sexual orientation, like you might ask any other question that has some bearing on understanding an SF work. It is of course a sensitive subject, bound to attract both trolls and overreaction against them, so we must tread with caution.