PSA: If a probiotic is on the shelf, not in a cooler, it's probably not worth buying. The best companies certify the count of organisms at time of manufacture , but no counts are guaranteed at the shelf. Probiotics are living organisms and ought to be refrigerated for max lifespan. You can get refrigerated probiotic supps at a place like Whole Foods. Source: I used to work in the industry.
When I asked my doctor about which kinds of probiotics are most effective she specifically mentioned refrigerated vs non-refrigerated is not a way to identify quality or effectiveness unless you know the specific strain(s) needed cannot be made shelf-stable. This lined up with asking my endodontist after they prescribed some antibiotics for a tooth infection. They did warn that the use by dates are a bit bull, not to stock up on them as they do deteriorate in quality with time, and not to try to keep even the shelf-stable ones above room temperature.
Maybe I misunderstood what my doctor said, maybe my doctor was just wrong, maybe it's actually extremely nuanced, maybe it's something I hadn't even considered. I guess all I'm saying is it's probably better to talk to your doctor(s) about it than follow self-sourced (in both the above and this comment) medical advice from HN.