It's not recommended to refrigerate xanthan gum because it can cause the xanthan gum to absorb moisture and start clumping up which makes it harder to use.
So you should not store xanthan gum in the refrigerator but you can do so as long as it was fresh when you put it in the refrigerator.
Refrigerating the xanthan gum can allow you to use it beyond it's use by date but be aware that it can clump up and you may have to put it in a blender to turn it back into it's original form.