Not sure why. We already have a term for organized religion, so I'm pretty sure disorganized is also an option. Plus, the more you basically demand that it has to be exactly like whatever you grew up with, the more you exclude actual world religions from being a religion.
E.g., Shintoism is pretty much the national religion of Japan, and it was very much the official religion in WW2. And it's a much more disorganized religion than any flavour of Xianity ever was.
For a start, you don't need any special qualification to have your own shrine, other than having enough people take it seriously, and it can be yours to minister just because you inherited it from your mum and dad. There is no shinto pope or bishop to tell you that you're doing it wrong, or that you need to get any approval from. If people still think that your fortunes (as in strips of horoscope-like predictions) are worth getting, congrats, it's as much of a shrine as anyone else's. And it can have started over as little as that some farmer thought some fox helped his family, and made a couple of fox statues, and other people came to pray to the fox messengers of the gods, and that was it.
And you need absolutely no qualifications whatsoever other than being unmarried and female to be a Miko, sometimes translated as shrine maiden, but basically more like an auxiliary priestess. In fact, historically it used to mean more like shamaness. (And technically is written as a female medium.) In the meantime, it's just whoever wants to play that role for ceremonies and such. If you're a priest by sole virtue of having inherited the shrine, you can have anyone be the auxiliary priestess just because she's willing to put on a traditional miko outfit and play along. You can dress your daughter up during ceremonies, and congrats, she's a priestess.
Quoth Lucky Star, "Hey, you too cosplay priestesses at your family's shrine."
It's played for laughs, but basically literally that is all the qualification needed. If you're willing to cosplay one at the shrine, and the shrine owner is ok with it, congrats, you're a miko. No different than putting on a maid outfit at a maid cafe.
And you don't even have to do that permanently at one shrine, mind you. They actually have thousands of years of the tradition of traveling mikos. So basically some priestess from out of town could just show up at your shrine, and if she's famous enough or you're otherwise ok with it, congrats, she can cosplay a miko at your shrine over the weekend.
Hell, in the meantime some major temples have started offering foreigner tourists the chance to work as a miko for a few days, if they're willing to pay for the experience.
Temples are also very much not important, other than as historical buildings. The important part for religion is the shrine within, which may literally be nothing more than a donation box and a bell with a rope. If some big noble wanted to build a big golden temple around his favourite shrine in his capital (which actually happened, btw), he's free to, but it doesn't make the actual shrine any better or worse than the one in someone's back yard, two blocks down from your house. I mean, the big one will get tourists bussed there, but that's not a
religious difference.
They also pretty much just have a loose collection of legends, but not much in the way of actual doctrine/ideology or standardized prayers or anything. A "prayer" can be and usually IS no more than "please help me pass the exam." Then you chuck a 100 yen (about 1$) coin in the donation box, or however much you feel you need to offer, clap your hands and/or ring the bell, and you're on your merry way.
But generally, they have SOME religious customs (such as you stick a pair of chopsticks into the bowl of rice at a funeral, but it's a horribly insensitive faux pas to do that at the dinner table) but none of them really is some standardized religious doctrine.
So would you say that Shinto is NOT a religion? Surely something with tens of millions of followers, and which was the official religion of a country (in fact, a world superpower) at one point, might be reasonably argued to qualify as a religion.