You can use vinegar and baking soda in carpet cleaning, but not at the same time. The cool chemical reaction used in 6th grade science class volcanoes has no value for cleaning. However, independently, vinegar and baking soda are useful. Vinegar is a fine disinfectant, possessing a pretty impressive germ killing ability. It’s not as strong as bleach, but it’s certainly less abrasive and easier on the nose. Vinegar is also helpful in cleaning up pet accidents (although I prefer hydrogen peroxide). Speaking of pet accidents, baking soda’s best use is as a deodorizer. Sprinkle it over the smelly carpet at night and vacuum it up the next day. Just as the open box in your refrigerator does, the sprinkled baking soda will absorb odor. If the desired result isn’t achieved, do it again. You won’t hurt anything.
All that said, keep in mind that just as with your dishes, laundry, and hair, you need soap and hot water to actually clean your carpet, and this is best left to professionals. If you must do it yourself, natural supplies such as white vinegar, hydrogen peroxide, and baking soda are preferable to soaps and chemicals in DIY carpet cleaning because they do not leave behind residues that attract dirt. Ever hear that carpet cleaning makes your carpet get dirty faster? This is only true because of these residues, which create a tar pit, and every dinosaur that walks by is going to leave a fossil. This problem oftentimes occurs as a result of DIY cleaning and poor “professional” work. Professional carpet cleaning technicians who do the job properly will rinse out soaps and chemicals along with dirt and spots, leaving only clean carpet behind, which won’t get dirty any faster than it did before (barring any rogue meatballs or sick dogs).