I have let others use my card, and I have asked to use cards from others if I don't have my card with me for some reason. I've never had anyone say no. At one grocery store in the area, the cashiers have a card they can swipe for you. At another, the cashiers have said they're not allowed to swipe a new card for me, but that if someone in line let's me use theirs, they can swipe that person's card for me - so I ask. The person behind me gets more points to use for gas, and sometimes it add points to their card for other promotions, like a coupon that generates for free milk, or when they offer a free ham or turkey with purchases at Christmas. I get my purchases at a slightly lower price. It's a win/win situation.
I am not the least bit offended by someone asking - doesn't seem like a very personal thing at all. It's not like they're asking for a credit card or asking me to purchase their groceries for them.
I would be offended by someone intentionally and/or repeatedly asking for an employee card hoping to get an employee discount. I wouldn't be offended if it was someone who was simply asking for a grocery store card and didn't realize my card was somehow different. Either way, I'd decline politely.
I wouldn't be offended if someone asked for my lipstick, either. I'd think they were nuts, say no politely, and laugh about it later with my mother, who gets a kick out of all the crazy people I've run into in stores. She says I'm like a magnet!