As a big fan of the show, and as one who studies sociology and psychology, my own personal theory on the show's widespread popularity is how outside the norm something like this is.
it manages to combine the things demonized by other males (on the basis that we're, as expected by general society, supposed to be masculine and avoid things feminine) with attractive qualities that aren't usually accompanied by shows of the same nature, as in ones that are feminine and somewhat childish.
MLP:FiM manages to be straight up cute, positive, and fun while still offering developed, relatable characters, appealing animation, professional voice work, decent writing, clever humor, and mature/sensible dialogue. as well, the characters avoid perpetuating norms stereotypes that are usually associated with "girls" entertainment, they have realistic flaws and desires, making them more relatable. These are qualities that are unexpected to be found in a show with such feminine overtones (as is the case where "girly" is often associated with "lame" or low quality). but because they were present, appealing to us and entertaining us, it allowed us to ease into the feminine aspect, allowing us to accept and even adhere to it.
It's that aspect, that I feel, is what compels so many of us males to fall in love with it, because it's so outside the norm and different, as if it's satiating a craving we've been deprived of, due to the expectation of us to be masculine.
To test this, I'v tried multiple programs with the same girly, sugary, feminine overtones, such as strawberry shortcake, to see if I enjoy those just as much. Instead, I found them to be rather revolting, mainly because they're just so poorly made and of low quality, in almost every respect of the word.
I would also like to note that the difference in cultures may also factor into the phenomenon as well. people from certain countries and regions, where gender stereotyping and gender roles aren't a norm, seem to be more easily dissatisfied with the cartoon, while people from other places, such as general american society, where gender roles and stereotypes are more dominate, are more prone to embrace it.
that's just an observation of mine however, I haven't enough research or evidence to fully support that notion.