What effect, if any, does the use of probiotic supplements or probiotic-containing foods such as yogurt and kefir have on the immune system?

Healthy GI system. Leads to absorbing nutrients from the foods you eat. Reduces risk of inflammation in all other organ systems.
It can be beneficial. It can reduce unhealthy bacteria & add in probiotics/ healthy bacteria and yeasts. Kefir provides healthy probiotics (like Lactobacillus, Lactococcus, & Bifidobacterium, bacteria & yeast. It contains: Vitamins A, B1, B2, B5, B6, B7, B9, B12, C & K, a well as minerals like calcium, phosphorus, magnesium, potassium, iron, zinc, manganese & copper as well as amino acids like lysine, phenylalanine, r.