Pretty much what has been said before, though it has to be noted there's a not so thin difference between what happened in Shakespearean theater and Kabuki: while in the former the obligation of using young boys for the female parts was mainly just that, a matter of fact, in Kabuki men acting in female roles quickly became an icon, a refined form of art in itself, a philosophy per se, in a typically Japanese fashion. Much like any other form of art, it often was a family legacy (in the Japanese meaning, as even an apprentice would inherit the master's name as if he was his son), it had specific rules and symbolism, and it was regarded as more feminine than a real woman could ever be: the common rationale was that a woman could never be that graceful. I know it sounds paradoxical, but that's how very often the arts were perceived in Japanese traditional culture.
That being said, I'd dare to assume in the Japanese collective thought the cross-dressing male can still be perceived as relatively less of a taboo than we do. The fact Japanese young males can also often pull it off better than us, as they are at times genetically more inclined to have quite the androgynous look, maybe also helps, for two reasons: to us it tends to look "gross" as it's usually evident we are looking at a male dressed as a woman (and as such it is perceived as "out of place"), to their eyes it can be seen as less "disturbing" as it can be aesthetically consistent; for that same reason, it is also slightly more believable that a crossdressing male could really be mistaken for a female, so it's easier to pull the stereotype in an animated fiction without endangering too much the viewer's suspension of disbelief.
The opposite, a female crossdressing as a male, I'd say is found interesting for the same reasons we do: nowadays it is often perceived as hot as it represents a strong symbolism of the female emancipation. As anything that is culturally "unusual", that is a break from the previous canon of gender role, it can spark a so called "fetish". In Japan - where various fetishes are also particularly taken to the extremes - it can also have an even stronger punch, as the role of the female was - and to an extent still is - especially submissive.
To me, for instance, a woman wearing a necktie looks quite suggestive, sexy, and I'm sure I'm not the only one. If I were born in Japan, where the icon of the "ideal" woman in their imaginary still tends to be that of the husband's meek and passive servant (fun fact: you know how goshujin-sama means "master", right? It's not a coincidence that they have that western maid fetish, after all. Anyway, literally, goshujin means husband), I would probably perceive it as even more suggestive.
There surely are also many other reasons why they often find this cliché interesting to use even not necessarily for purely comedic purposes (though those are nowadays the easiest to pull, of course). For instance, let's not forget how several of their shinto deities were ambiguously sexualized, like Inari. It all adds, little by little, into building a certain collective unconscious, Jung would say. While it is a "taboo" there too, and it is played with as such, there's also the fact it isn't a taboo for the same reasons as ours: ours originate from religious dogma, as any form of gender bender is considered a sin against God and is a theme extremely prevalent in the scriptures. Theirs is more rooted in simpler social customs, so it's also easier to play with in a lighthearted spirit (that could also be why they tend to go heavier on it than us in their humor: as the taboo is less "severe" it has to be broken more blatantly to be as irreverent; the comparison between "our" glam rock and their visual kei mentioned before is quite fitting).
Still all these differences are relatively minor, imho, and I'm not even taking into consideration how much the post-war era of newborn cultural contamination they undergone has had an influence on the matter.
