Everyone loves a natural home-cleaning solution, not least because you've likely got the ingredients in your pantry already. Bicarbonate of soda and vinegar are two of the most common components and if you've ever seen a science fair volcano, you have a sense of why.
Independently, bicarb soda and vinegar are great for home cleaning -- bicarb soda for its scrubbing power, vinegar for disinfecting and odour-elimination. And you often see them suggested in tandem for cleaning out slow drains.
It seems to make sense -- get the effervescence of that papier-mâché volcano into your sink and let the bubbles blast through the pipes. And it feels so satisfying, too. You dump some baking soda into your drain, then pour over a bunch of white vinegar, and swoosh, all those bubbles make it seem like something is happening.
And something is happening. But not deep in your pipes where the clogging gunk is.
Basically, all or most of the reacting happens right where the baking soda and vinegar meet. And even if the reaction does get down to the gunk, this experiment shows that it's not going to do much.
If you'd still rather avoid the Drano, try boiling water with a little dish soap (for oily buildup likely in kitchen sinks... or the bathroom sinks of people who use oil cleansing on their faces) or boiling water with salt. This post from The Kitchn has more on why those methods work, and how to avoid greasy clogs in the first place.
If you're dealing with a bathtub clog, that probably means hair and bicarb soda and vinegar aren't going to do squat for that, either. If you're not squeamish, your best bet is to snake your drain. And if you are squeamish, find someone who can do it for you.