What idiosyncrasy does your pet have?
Is your cat afraid of water? Baths are not necessary for cats, they will self lick themself clean. But you could try a wet cloth for a spung bath type.
Sometimes it could be the area where the bath will take place, like a bathroom tub, or a kitchen sink, or a garage wash tub. Maybe the pet would like to get washed outside in the yard with the water sprinkler, or after the kids are done using the baby pool.
What is your pets reaction to the sound of a hair dryer? If the pet is absolutely terrified of it and runs away, this would be your clue NOT to take your pet to a groomer who will use a hair dryer to blow dry his fur.
This would go for the vacuum cleaner too. Some animals are scared of this sound and will want to hide. It is important for you to know how your pet will react to gun shot/big boom sounds like if you drop something or when fire works go off. If you are out on a trail hike walking your dog without a leash on, he could run when the sound occurs. Even the sound of a car when it back fires.
Is your dog absolutely afraid of men, then don't put it in a position to be around a dominant man, because it may have been abused by one.
You need to look for fears in your pets to make sure their life is a safe one, and your home is a safe place for them too.
Respect and love your pet enough to really know what scares them or their fears.
This should also be information you would pass on to a groomer, or someone else who may need to care for the pet, or even if they day comes when you turn them over to a shelter.