I think there could definitely be, for example, a "whitesplaining" term, although I'm not the person to decide that. I have seen an awful lot of white privileged explaining times, particularly in regards to how the white person with their clearer, more objective understanding, can prove that X is not racist, silly PoC. Tolkien was writing in a different era! Mammies are positive stereotypes! There are PoC in the future I've imagined; they're just off doing something that doesn't get shown in my book! But it also comes in things like, "If you people would just stop being victims..."
I've also seen behaviour that might equate to cisplaining (you're just confused), straightsplaining (I don't have anything *against* you people, but if you can get married it violates the separation of Church and State) and from years of living with my brother, I have seen plenty of, and many times engaged in, what could be called ablesplaining* (what you need is a good hiding to set you straight).
But I don't like "douchesplaining" as a catch all. It's not just people being ignorant and condescending, it's people doing so through the mechanisms of privilege supporting their superiority in a given situation, even though, on the topic at hand, they have an inferior understanding. Using a term that notes the privilege is, I think, essential to calling out the perpetrator not just for bad behaviour, but for behaviour that is sourced in and enforces that privilege.
Also, "douche" in itself is an insult, and it is a gendered insult (in the feminist circles I frequent, a "douche" refers to something that is fundamentally unnecessary and harmful to women; in the wider world it means "something women put on their disgusting and inferior genitalia").
Being a man isn't bad. Neither's being white, middle-upper class, educated, cisgendered, straight, or (for now) typically able. It's the man(etc)splaining that's the problem: bad behaviour as an exercise of privilege.
If you really want a word for people doing this shit to each other when they share the same privileged status or when privilege is not an issue - and I'm sure it happens, though maybe not as often as you might think - "assplaining" would probably work fine. Asses are a near-universal source of toxic emissions.
The thing about mansplaining is that it's not obviously discourteous. Dudes will often mansplain very politely - by the standards of politeness that are enforced by patriarchy. They won't raise their voices or call me a cunt or a bitch, they'll just politely and ignorantly explain to me shit I already know, or point out how I am wrong and they are right. Which of course makes me the aggressor the second I call them on it. I want a term that focuses on the behaviour, and doesn't let courtesy act as cover for sexism.
* There's also a particular form of ablesplaining that gets directed at companions as a sort of person-by-proxy: "Does he want an icecream?" "Why don't you ask him?" "*affronted look*"