There are a few instances when you should not drink kefir. If you are lactose intolerant, then drinking kefir can cause some uncomfortable side effects like bloating, gas and diarrhea. If you have an allergy to milk or any of the other ingredients in kefir, it's best to avoid it. Kefir also contains a small amount of alcohol, so if you're avoiding alcohol for personal or religious reasons, you may want to steer clear of this probiotic-rich beverage.