In the case of strip searches, if she's young I would object because I don't want her growing up thinking strangers touching her naked is acceptable in general. I would require some level of maturity first to be able to understand the moral difference between a strip search performed by a TSA officer on duty and one performed by her 4th grade teacher.

In the case of scanners, under the same assumption of completely professional conduct, I see no problem. She would probably be more emotionally scarred by a visit to the doctor.

Kids generally don't have any problem running around naked. It's the adults that feel self-conscious.