Should a caregiver shop for themselves on mom's time?

When you say “on moms time” it sounds like it could be a problem for you.
Extenuating circumstances might make it an easy yes or a hard no.

As long as the patient is being tended, is a shopper, might even be entertained by it, doesn’t mind waiting etc., I might think why not?

It could go wrong, or it could be perfectly fine. Would depend on stage of patient, tendency to wander, aides other responsibilities that may or may not be accomplished for the day, etc. How often it would happen. Very open ended question.

And in these days one has to remember COVID. I wouldn’t want my mom in a store any longer than necessary.

When my husband's caregiver takes him shopping I always tell her to do her own at the same time if she needs to.

I suppose it depends on the situation. A caregiver’s primary responsibility is to their client’s needs. If they tell you it’s okay, I suppose that it would be okay.

If the caregiver is taking Mum shopping, I would have no problem at all with them picking up their own shopping at the same time.

Nope.