That is VERY unusual. They are supposed to ask you to remove the baby from the sling because the slings need to be x-rayed, similar to why they ask you to remove the laptop from the bag.

You can carry an infant through with you, only once they start walking they need to go through themselves and you follow.
6 flights so far and haven't had to remove her. Not sure whether the security staff could see by looking at the slings that they were all material based.