"If you live in a home that has an hoa do you consider the shells such as hazelnuts left by squirrels on the green belt litter and worthy of violation fine"
You need to check your state and local statues, as well as your HOA CC&Rs for any law or rule against feeding squirrels? Does your HOA CC&RS have a specific rule stating that it is a violation to feed squirrels? The vague nuisance rule will not hold up in a court of law. If a law or specific rule does not exist, then who are you going to fine, the squirrels? The homeowner is not in any violation.
Furthermore, if your HOA allow homeowners to have bird feeders then your asssociation is allowing the feeding of squirrels and other wildlife. Do your rules restrict what kind of bird food can be placed in the feeders? Squirrels are not the only animal that eat hazelnuts. Blue jays, woodpeckers, and nuthatches are just some of the wild birds that enjoy nuts in shells and have the ability to crack them open. These birds will also hide the nuts, just like the squirrels.
Your HOA should just relax and enjoy the antics of the squirrels. Hazelnut shells are natural and biodegradable and are currenly very poplar as mulch. I read that Martha Stewart uses the shells has part of her landscaping. Relax and leave the homeowner and squirrels alone or you might windup in court.