Gremlins/WMG

The Shop was the Pet Shop of Horrors.
Confirmed from the manga's point of view, more or less - Count D is seen selling something in a box that sings quietly to itself, and he tells the customer those three rules within the first few pages of volume one. Being D, he's smug and amused that it all went horrifically wrong, and he is not helpful in the least.
 * It's possible that the person the mogwai was bought from at the start of the movie was the young  D that was born and we meet briefly via Chris at the very end of the first series.

The alignment of mogwai depends on their origin.
If a mogwai (or possibly gremlin) is subjected to water against their will, then the resulting puppies are "evil" because of the trauma the original mogwai was put through. If a mogwai is prepared or has a proper partner, and is able to focus on their alignment or offspring, then the offspring are good or the same alignment as their parent. The other mogwai all turned out evil because Gizmo is single, asexual, adolescent, or just plain didn't want kids.

Gremlins are not Exclusively Evil.
We've only seen "evil" mogwai aside from Gizmo, and Gizmo never had food after midnight. Who's to say that good mogwai wouldn't turn into good gremlins?
 * Perhaps when "good" mogwai willfully eat after midnight, they turn into whatever Yoda is? See Below.
 * Perhaps only one Mogwai per "litter" is evil, and the others are completely neutral until they become Gremlins? The unnamed Mogwai in the first film pretty much did whatever Stripe told them. (Billy even commented on it.) In the second film, Lenny and George didn't act until Mohawk commanded them, and Daffy was pretty much Chaotic Neutral throughout the movie. Perhaps if you can eliminate the "bad seed" Mogwai from each batch, the others can be turned to good like Gizmo?

The Christmas presents scene in the first movie was a commentary on the rise of modern technology usurping the place of traditional entertainment.
The new mogwai are all gathered around and fighting for control over a miniature arcade machine. Gizmo is playing a toy trumpet, and one of the other mogwai either spits at or intentionally projectile vomits at him in disdain to make him stop. The modern technologies are crude but popular, and they overshadow more traditional venues which, though they may be performed by less talented people, have heart.

Mogwai are Exclusively Evil.
Gizmo is an exception, or the First mogwai.
 * The Novelization suggests that the original Mogwai (created by aliens to serve as pets) were full of Incorruptible Pure Pureness, but that something in their genetics was bugged, and each new generation is a little more Chaotic Evil. Gizmo is something of a throwback, so he's nice, but his offspring are almost inevitably terrible.

The Shop was The Little Shop That Wasn't There Yesterday.
The dad wasn't able to find the shop without bribing the kid to tell him where it was, and it was most likely in Chinatown, in San Fransisco. In the second film, the shop was in New York in what appeared to be an English-speaking district. The shopkeeper wouldn't sell the place; but if he had only been there for a couple of years, why wouldn't he? The answer is, he didn't move- the shop did. When he died, the shop became a perfectly normal shop that could be destroyed by a wrecking ball.
 * New York has a Chinatown, as do a number of other U.S. cities. There was no indication that the shop was anywhere near San Francisco during the first film. Fail.
 * No need to be so harsh. And while your point is valid, it doesn't disprove the original theory. While the shop could have always been in New York, Mr. Pelzer might very well not have been able to find it without the grandson's help, and it was Mr. Wing's death that took away the shop's magic and allowed it to be found and torn down.

The Gremlins (and possibly mogwai) are arthropods, not mammals.
The "fur" is soft spines used for identification (why Stripe and, until Brain Gremlin, Mohawk were the leaders of the Other Mogwai and gremlins); the skin is a soft but tough material, analogous to an insect's skeleton in the way that a snapping turtle's is compared to a slider or tortoise. Seriously, just look at the first shot of the pods, the hatching, and their fingers.

Mogwai in their mature form look like humans.
The shopkeeper's mouth puffed out and wrinkled like Gizmo's when he said "I told you so" at the end, and had the hair sticking out everywhere. Gizmo can make sounds in English (most notably, "uh-oh"); and if Gizmo is the shopkeeper's son, and the other mogwai are evil because Gizmo is an adolescent as in the guess above, it kind of makes sense.
 * This also creates the option of all elderly wizards with no past being mogwai.

Mogwai in their mature form look like Yoda and Yaddle.
Shave a mogwai and paint it green. Yoda. The living-on-Dagoba thing was possible because either Mogwai grow out of the multiplication when continually exposed to water or Yoda's just that good. (He's also an elderly wizard with no past.)
 * It makes more sense for a Gremlin in its mature form to look like Yoda because they're already green and hairless. Yoda does seem to have some semblance of white hair on his head, so for all we know, he was a Gremlin leader once. In the spin-off novel, Gremlins were said to have been accidentally created by an alien scientist; there's your outer space motif / link for ya.
 * One problem: Yoda lives on a swamp planet. No way he could keep from getting wet. Why isn't the place crawling with his offspring by now? Of course, it's possible that Yoda's race were the "alien scientists" who created mogwai/gremlins in the above novel; perhaps some kind of genetic engineering experiment, an attempt to create a perfected form of themselves?
 * I find it more reasonable to say that Yoda species designed gremlins. Maybe they started genetic manipulation from a creature that was to them like the chimp to the human, a smaller less intelligent and furrier version. Otherwise, maybe Yoda is just to old for breeding.
 * He's not only a frickin' Jedi, he's the frickin' Jedi. You see him fight Tyranus? Now, instead of plasma swords and lightning that he has to avoid, it's water. Yoda could do it.
 * Perhaps when a "good" mogwai willfully eats after midnight, rather than an Exclusively Evil gremlin, it transforms into a talking "magical" (i.e. force sensitive) whatever-Yoda-is?
 * Maybe someone in service of the Sith tampered with the genetics of Yoda's species to add in the genes related to the "rules" - water, light, after-midnight eating, and then released them back into the environment to interbreed until the genetic stock of the species was compromised and chaotic evil reigned, then Yoda had to more or less commit genocide on his own kind to get rid of the Gremlin taint, which is why there aren't other Yoda-like creatures running around in the Star Wars galaxy. But he had a son or grandson Mogwai that he didn't want to destroy - that would be Gizmo - so he sent baby Gizmo away in a stasis pod, which traveled millions of light years across the universe and landed on Earth, where it was discovered by the Old Chinese Guy or one of his ancestors. Yes, Gizmo is a Jedi. His badassery at the end of Gremlins 1 and 2 only hint at his potential.
 * TV Tropes Made of Win Archive.

Grandpa Fred is Palpatine
And he was the one who was really behind. Also, Dr Catheter survived and hitched a ride from the aliens who created the Mogwai (in the book) to a galaxy far, far away, gaining the power to project electricity from his fingers.

Parts of the story were ghostwritten by David Icke.
The Brain bears a suspicious resemblance to former Australian Prime Minister John Howard. Icke believes most of the world's leaders are reptilian creatures from outer space (in the book, the Mogwai were created by an alien scientist). Coincidence?

Mogwai reproduce sexually to produce "good" Mogwai, and reproduce asexually through water to produce "bad" Mogwai
Gizmo is the product of a male/female sexual relationship. There are female Mogwai around somewhere, but are very rare.

Mogwai are based off a real animal, at least partially
They closely resemble tarsiers in their appearance.

Murray Futterman's stories about gremlins during World War II actually happened.
They may have been the same gremlins as in the movies.

Mr. Wing left his home country China when the Japanese started attacking. He took the Mogwai with him. On his way to America, Gizmo accidentally gotten wet and eventually came gremlins. Those gremlins may have gotten into American planes stationed in some countries along the way.
 * The Novelization implies, but does not state, that this is so.

Gremlins are a sub-species of Orkz.
They are basically smaller, animalistic Gretchens. They are also Exclusively Evil and naturally have some knowledge about machinery (which they use for sabotage), like an Ork. And they're green, just a little darker...