(I realize this answer is mostly a compilation of comments and answers to other questions, but I'm having a hard time sorting through it all...)
I think the Wikipedia definitions are a great starting point:
"Science fiction is a genre of fiction dealing with imaginary but more or less plausible (or at least non-supernatural) content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities."
"Fantasy is a genre of fiction that commonly uses magic and other supernatural phenomena as a primary element of plot, theme, or setting. Many works within the genre take place in imaginary worlds where magic is common. Fantasy is generally distinguished from the genres of science fiction and horror by the expectation that it steers clear of scientific and macabre themes, respectively, though there is a great deal of overlap between the three..."
And combined with Gilles' answer here:
I suggest the following guidelines (improvements welcome):
1. If it's marketed as SF, it's on-topic.
2. If magic, futuristic science or technology, alternate history, or other
sf-nal concept is an important part of the overall plot, it's on-topic.
(Alice in Wonderland, Clockwork Orange, etc.)
3. If the question is specifically about an sf-nal element, even if it's only
a minor part of the work, it's on-topic.
4. If it's set in an on-topic universe, it's on-topic.
5. If you're not sure it's SF but you think a good case can be made for it,
6. If there is a minor supernatural element (e.g. a fortune teller's prediction
comes true, or someone sees a ghost, or a story for children involving
anthropomorphic animals) but it's just a throwaway plot element that's
not particularly relevant to the question, it's off-topic.
(Finally, my own contribution:) I think some elaboration of rule 1 is necessary, and I think that's where the difference of opinion comes from.
If it's marketed as SF/F and/or if the author considers it SF/F, then it's on-topic.
If the author doesn't consider it to be SF/F, then it gets tricky. Vonnegut didn't like being considered an SF writer, but many people consider some of his work to be SF and I'd consider it to be on-topic.
OTOH, there've been questions about stories in The Bible, and I'd consider those off-topic because the vast majority of people who are interested in The Bible don't consider it to be fantasy, despite some fantastic elements.
I think that if the author doesn't consider it SF/F or if it's marketed as something other than SF/F, then it takes a clear contrary opinion of fans (or, in this case SciFi.SE members) to make it on-topic.
And that's the grey area MLP:FIM falls into. I think it (probably) wasn't considered as fantasy by its creators, and even if it was, the themes and plots are largely the same as any other kids' show - broadly, teaching them what's good and bad.
But since most SciFi.SE members are ok with considering it to be on-topic, and since it does fit the objective criteria to be considered "Fantasy" then it's fine. Personally, I think it is a borderline case, but I'm happy that others consider it on-topic.
It's worth pointing out that the themes of Friendship Is Magic are exactly the same as the previous generation of My Little Pony ("Ponyville") shows and movies but there are no questions about those shows. The MLP Ponyville movies have magic, and dragons (well, just Spike), and Breezies (a sort-of butterfly/pegasus/pixie creature), but they don't have the writing that appeals to adults, so I don't think even the most hard-core brony is interested in them. (I've got a daughter who's the target age for all things MLP, so I've seen almost all of them!)