"Sell-by" dates are pretty arbitrary overall - consider more a "check-before-using-after-this" date. Pour out a spoonful and if it looks, smells, and tastes alright, you're good to go.
Sorry, it's early here and I conflated "sell-by" and " use-by" dates in my head. Sell-by dates are even MORE forgiving; you'd be fine waiting at least a week before you'd want to start checking it.
It depends on how it's been made.
Ff it's cultured (and not pasteurized again after being fermented) then it should last several days after the sell by date. This is usually what they sell as buttermilk. It should just become more sour as it ages, instead of the sudden putrid off smell that pasteurized milk has when it's past it's prime.
Now, if it's actual buttermilk, ie, the milk leftover from making butter, it should be good for a day or two past the sell by date.
Now, if it's acidified milk made to resemble buttermilk from making butter or cultured buttermilk... I have no idea.
Trust YOUR senses. If it's off, it will smell off. When in doubt you can toss it out, or try a small sip and wait to see if it upsets you. But usually, the smell will tell you. Sometimes commercial milk go off BEFORE their expiry and sell by dates. Never trust milk without smelling it first.
Traditional buttermilk will last a long time after the sell by date - I've used it as long as a month afterward with no discernable off-flavor or degradation of quality. In fact buttermilk was traditionally used more often in the South before refrigeration because it would keep so much longer than fresh milk. For this sort of product, the smell/taste test is sufficient to see if it is still suitable for consumption.
Usually a couple weeks. Smell/taste. You can also freeze it.
Unopened, I have found it fine even after 2 or 3 months past the exp. date!
p.s. and if you open it and it does taste bad, there are substitutions that are good: yoghurt, or milk+white vinegar. You can also buy powdered buttermilk (to keep in your pantry) and add to water.