Why We Bother Checking
For people with coeliac disease, gluten isn't just uncomfortable, it triggers a genuine immune reaction that damages the gut lining. That's a different league of seriousness compared to a mild sensitivity, and it's why gluten-free labelling is actually regulated rather than left to marketing teams to decide.
Plenty of people without coeliac disease still feel better avoiding gluten, or simply prefer to for personal reasons, and that's a valid call too. Either way, a supplement is meant to support your routine, not quietly work against it because nobody checked what the capsule shell was made from.
For the official picture on coeliac disease and gluten, see the NHS page on coeliac disease, and for how gluten-free labelling is actually regulated in the UK, the Food Standards Agency's allergen guidance is worth a look.