You don't always have to rinse after cleaning with vinegar for some things.
However for other things that you clean with vinegar such as tile, grout or when using vinegar for things like deodorizing carpets you need to rinse after cleaning with the vinegar.
If cleaning things such as floors, including hardwood floors, laminate floors and vinyl floors rinsing after cleaning with vinegar is not required.
You also don't need to rinse after cleaning with vinegar if you're cleaning non stone countertops or even when cleaning glass, mirrors, sinks etc as the vinegar will evaporate naturally without leaving any residue.
If cleaning dishes with vinegar you should rinse the dishes to remove any vinegar taste and keep the vinegar taste from getting into the food.
When you're cleaning tile and grout using vinegar you need to rinse the vinegar away with water which also reveals clean tiles and grout.
And when you use vinegar to deodorize carpets you may need to rinse with a diluted vinegar solution "1/2" cup vinegar per gallon of water after you shampoo the carpet to lift the soap residue.
Or if you use vinegar to remove any hard water stains, you may want to wipe away any excess vinegar with a damp cloth.
Vinegar is a good natural cleaner for most things although use of vinegar for cleaning some objects may dull and scratch the surfaces or even corrode surfaces.
Vinegar has a very low pH level that means that the vinegar is very acidic, so the vinegar can corrode some surfaces over time.
Using vinegar on natural stone such as granite or marble can dull and scratch the surface and can corrode surfaces such as unsealed grout, window seals, and even refrigerator and dishwasher gaskets.