It depends. Most newer carts are designed so that the hook that latches the seat into the carseat base, will hook on the cart and lock the carseat in place. You have to unhook it, just as if you removing it from the base to get it out of the front section of the cart. If that’s what the mom is doing, then the baby is quite safe. Older carts, or plastic ones like at Target, don’t allow for this, so then it’s safer to put baby in the cart or wear the baby.
That is what I'm saying. To heck with the groceries. Ware the baby.