I would be interested in serious studies done to see if there is a causation between the vaccines. I do believe with some behaviors it is plausible, but there has not been enough research done to say for sure. I believe the vaccine might exasperate underlying issues.
With Skye, I did the rabies vax one year and she immediately (within a day or two) started with a little hair loss around her eyes. They were a bit swollen and watery. It took probably a month to go away. The next year I had to do another rabies jab...same thing, except it hasn't really gone away but gets better and worse. I've just been told it's allergies. Now I did do the vax in March each year (Springtime, stuff is starting to bloom, causes allergies) so who knows.
A few days after rabies vax for Zoie one year in particular, her lyme disease flared up majorly. It didn't happen the next year.
A vaccine challenges the immune system, so it can certainly trigger immune system-type issues. ie; an allergy flare up, or flare up of an existing condition. This is why a pet should not be vaccinated when it is sick. The rabies vaccine does seem to cause more issues than some. OTOH, the disease it prevents is a particularly deadly one, and is a health risk to humans, so I'm not personally willing to gamble with it. My dogs are vaccinated for rabies. (also for distemper and parvo)
I had a dog have a mild reaction to the rabies once. And I was disgruntled about it, because he hadn't needed that vaccine. The year before, I'd taken him to a cheap veterinary chain to get his rabies, because I was low on cash, and didn't want to skip it. They vaccinated him, I went and paid, they handed me the certificate, and it was only good for a year. Which is wrong, he was an adult dog who had been vaccinated before, it should have been good for 3 years. I figured it was too late to do anything, but the next year when I had to get him a gratuitous rabies vaccine to stay legal, I went to my usual vet and paid the extra $50 or whatever it was. Anyway, we went to an agility trial the next day, and he couldn't run. Poor guy didn't feel good. He was okay the next day, but I've always kept it in mind since then that the rabies vaccine is a toughie.