Animal fur can go in curbside compost carts. 
Sunday was the spring shearing of our fluffy dog.
She fills up two kitchen compost bags, each 2.5 gallons so that’s 5 gallons of “waste” diverted from the landfill.
We’ve tried to leave fur out for birds
and other animals but it doesn’t seem to get taken and instead blows around the front yard. 
Otherwise, if you have takers it’s supposed to be good nest bedding.
We cut our own dogs’ fur and toenails, and express glands. The cost of a professional razor 
and clippers
was covered quickly in lieu of making appointments with a business. We have a blade for the dogs and one for my husband. When we had four dogs this saved time
, energy
, driving
, gas 
and money
. Herding four dogs and paying for all their upkeep was a lot so this is how we chose not to “waste” those resources if you are thinking in terms of reducing waste. We can also reuse tools, wash cloths, and compost the results of grooming instead of sending all that to the landfill
. These skills also allowed us to learn more about dogs, how they changed as they aged (e.g. bumps) and was good for bonding.
Our two dogs are now 15, one is blind and deaf, so grooming them ourselves, and having them be used to that, is such a blessing. It’s easy and stress free for our senior furry babies.
If you have the time and interest, I do recommend learning how to groom your dogs yourself. Other great options are to see if there are people in your neighborhood offering the service, if there is a local business that may be able to give you a bulk discount or a pre-scheduled discount. There are also mobile grooming trucks now that come to your house and can help alleviate anxiety in many dogs. That would be supporting a small local business as well. Small businesses may be able to incorporate greener practices into their business model due to scale of the business and limit on customers. It won’t hurt to ask and discuss with your groomer what tools and items they use when working on your pets.