I know you didn't quote me on this, but no, I wouldn't be mad if it were my mom or MIL. Maybe because we don't live near either of them so I know they want to show them off to their friends when they get the chance, but it wouldn't bother me.
In fact, 1.5 weeks ago was our youngest daughter's baptism. Now, she was almost a year old at the time because we moved across the country last year and couldn't get back to baptize her (we wanted to do it where my family is). But even so, my MIL passed her around to everyone, and people in my family and my mom's friends were dying to get their hands on her too. They don't see her often so this was their chance. And I gladly let her grandmothers show her off to whomever they wanted because it makes them happy and won't really hurt her. Yes, she could get sick (and she did! she actually came down with a nasty cold a few days later, but who knows who or where she got it), but even my husband who is a germophobe and a physician, was okay with random people holding her.