The themes in the early days of Disney animated movies were pretty simple boilerplate ones - good is better than evil, pretty people are always the nice ones, ugly people are always the mean ones, and if you lie you will turn into a donkey and get eaten by a whale (okay that last one was a little weird). But lately, Disney movies have found themes that are...well, WAY more mature and nuanced than anyone really could have expected. Namely Zootopia's focus on a kid's film that is explicitly about casual racism - as in, not overt KKK-style racism, but the subtler, more ingrained in social norms-style racism. It's incredibly well-done for such a tough theme, and manages to be hugely entertaining AND moving on top of it all.
It seems easy to argue that since most early Disney films were based on fairy tales, it stands to reason that the villains would be pretty one-dimensional. All the bad guys are usually just pure evil for no real reason other than that it's just their nature, from Maleficent going PRETTY OVERBOARD about not getting invited to a party to the Evil Queen in Snow White relentlessly trying to murder a young girl because she's prettier than the queen.
But in recent years, the villains have gotten LAYERED AS HELL. A great example of this is Tangled's Mother Gothel, who - despite being a fairy tale villain too - is one the darkest and scariest villains Disney has ever put up on screen, because she seems so real.
Mother Gothel's whole deal essentially boils down to being an emotionally/mentally-abusive, overbearing mother, cruelly undercutting her daughter to keep her passive and controlled so that Gothel can take advantage of her "gifts" for her own selfish desires. She doesn't want to kill Rapunzel or take over the kingdom or anything like that - she just wants to stay youthful and pretty, and even has some (tiny) level of affection for her (semi-adopted) daughter.
The character is complex and deeper than anything from the early days of Disney - here's what voice actress Donna Murphy said about Mother Gothel:
"I also think there is this thread of a kind of love that she does have for Rapunzel. It's not what she set out. But she does raise this child and it's the most intimate and certainly the most sustained relationship I think the woman has had in her 387 years or however old she might be. So as deep as the need is to get something for herself, she can't help but fall in love with her. She's spirited, creative, and charming and I think that stirs something in her that is confusing for Gothel. And Gothel has to keep reminding herself of what is most important, which is taking care of herself. But I think there is a genuine kind of humanity. It's by degree, it's not unconditional love but there is a love that develops."
The subtext in lots of old Disney films can be...regrettable. Lots of mildly (to way over the line) racist depictions, sexist norms, and nonsensical beliefs being reinforced. But modern Disney films seem to go out of their way to push for more progressive, positive bits of subtext throughout - namely the way Frozen depicts a young woman's struggle with "coming out" - which basically boils down to "accepting herself for who she is, rather than locking herself away and trying to hide from herself and the outside world." Of course, the metaphor here is "ice powers = sexuality," but it works surprisingly well.
4. Love Interests
It's tough to come down too hard on Disney for this, as this was just the way stories were told in the old days - princesses HAD to marry princes and all stories HAD to have a love interest. Unfortunately, most of these stories - from Cinderella to Snow White to Sleeping Beauty - have the title character end up totally helpless and completely dependent on a blandly handsome prince coming to save the day and being the ACTUAL hero of the story.
Nowadays, not so much - Disney's recently-released Moana doesn't have any love interest, period. It's about a young woman discovering herself and her place in the world, and a love interest would have just gotten in the way of that. An even better example might be Frozen, where the trope of the nice handsome prince is completely subverted by having him be the VILLAIN of the film (and while there is a love interest, it's not a huge deal in the film and takes up a pretty minor amount of screentime). And even when there is a major-ish love interest, it's still the title character who takes the initiative and winds up being the hero in the end (Zootopia might be a bit debatable whether Judy and Nick count as a "couple," but regardless of whether their love is romantic or friendly-only, Judy's ingenuity is what saves the day in the end).
5. Weirdly Hot Foxes
This is the one area where Disney has been remarkably consistent. WHY AM I GETTING KINDA TURNED ON BY THESE SLY FOXES?
So if you ever want to know how people turned into furries, remember: no matter what generation they grew up in, it's probably Disney's fault.