Either they were not properly educated about the importance of getting him vaccinated or, like so many, they did not feel it would happen to their dog and did not really feel it was important to obey this particular law. From the book and the movie, it was obvious that the dog's owner was the only one who really thought of Cujo as a part of his family. His parents were more like it was just something they owned, like property.

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one lick is all it takes!
No, "one lick" is not "all it takes" to spread rabies. It actually takes a fairly deep bite wound. The virus then travels through the muscle fibers into the nerves, through the spine and from there into the salivary glands. It can take up to a year to show symptoms after being bitten (though the vast majority of cases break within 6 months) because this travel along nerve pathways is so slow.
I would not recommend going out and getting licked by a rabid animal, but no, a single lick is not what spreads it. Needs to be a deep bite into a muscle from an animal who has been infected long enough for the virus to have spread all the way up to the salivary glands.

also my cats never go outside but if they did they would def get a vaccine if i had to get a vet to come to my house

when we had a dobeeman he was vaccinated against rabies but my cats aren't. i alway wanted to take them in for it but iw would be hell to put them in a carrier (been there done that and it took 2 ppl literally to hold one cat

Maybe he let the booster shot lapse, happens all the time. A dumb rabies animal is just as dangerous as a furious rabid, one lick is all it takes!
Spoiler alert for them spoil sports out there! Y'all like spoiled milk, stop crying over it!

Good question. I think that if Cujo was vaccinated for rabies then we would have never had this horror film lol
But seriously, maybe it's because the family may not have believed in vets - "it's just a dog" mentality. OR maybe it was because they had had very little money as you can see from the film. Several reasons as to why the his owner never had him vaccinated.
It's actually a good question you have - now you got me thinking about it
"I am invisible, understand, simply because people refuse to see me." ~ The Invisible Man

A lot of people don't vaccinate their animals. Especially if they live out in the country and don't have money laying around. My dad grew up poor in Alabama and 1) all cats and dogs lived outside 2) if your animal was severely injured or sick, you took it somewhere out of sight and shot it
What I find odd is Hollywood's depiction of rabies. Not that many rabid animals/people go all homicidal. You're more likely to just get really really sick, act irrationally (fear of wind and water), walk in circles and bump into things, then fall over and die. In the latter stages of rabies, you're too uncoordinated and out of it to be much threat to anyone's life.

You'd be amazed at how many people don't vaccinate their animals. The dad didn't seem like the type to want to waste money on things like that and the wife would never question him.

Our cat came home with half its fur missing from its face a huge gash on its head. Now that's a wound to worry about.

It was a big bloody spot on his nose. You'd have to be a pretty careless pet owner to not do something about it.

Wound? It was a scratch. Happens to animals all the time. I doubt they'd raise a fuss over a tiny scratch on such a big dog.
Does IMDB hate apostrophes?

Considering no one in the family noticed the wound on his nose or when he started looking bad then I'm guessing they didn't really care about their dog enough to get a rabies shot.

White trash what a terrible term. If they were black what would you call them. You shouldn't "attack" poor people like that.

It was heavily implied that the family was not only poor but 'white-trash'-like.
They likely just did what they needed to do to survive day to day.
The father was a white-trash wife beater, the wife put up with it, the kid was an out-in-the-sticks kid just trying to survive.
The kid likely didn't even know about vaccinations.
"I'd say this cloud is Cumulo Nimbus."
"Didn't he discover America?"
"Penfold, shush."

Well, it's pretty easy to get a dog. And if the dog has never been to the vet, then he would have never been vaccinated. Considering it was in the country, I'd say that would be the case.

That was never explained in the book or the movie. One explanation could be that the Cambers were uneducated on the importance of rabies or simply they believed "it won't happen to my dog"