Dear John,
A solution of vinegar and water used for household cleaning is not likely to pose a health concern for your cat or dog. In fact, most cleaners—natural or otherwise—are typically appropriate for use in homes with pets.
The key to any product’s safety is to always follow label directions. For example, if you’re using a product to clean your tub, and the directions advise you to rinse out the tub after application, please do so in order to avoid skin irritation or gastrointestinal upset if a pet steps in or accidentally ingests any solution still present. Similarly, using a mixture of vinegar and water requires proper dilution and application.
It’s also important to store any unused cleaning materials in a secure location and out of the way of your pet. Following these simple precautionary steps can help keep your pets safe and healthy.