I sometimes have children who experience separation anxiety when their parents are dropping them off for the day. It's a natural part of development, sure, but there are also things that you can do to alleviate a lot of those tears and fears.
I'm especially fond of tip #3 in this video: Commit to your Exit. Let parents know that it's not a bad idea at all to hang out for a few minutes while their child gets comfortable. I always welcomed that and it's so much easier on a child than drop-and-run. What I didn't enjoy, however, was when a child would get involved in an activity and was perfectly happy and then Mom or Dad would made a big show of leaving. A content, acclimated child would suddenly become stricken with sorrow after hearing, "OK honey, I'm leaving. Mommy's going. Bye. Sweetie? Sweetie? Look over here at me. Mommy has to go. I'm really leaving this time. Here I go. I'm going." Please know that if that's how parents are behaving at drop-off time, it's a trigger for their child's anxiety rather than a help and you should let the parent know about it and give them ideas about how to handle the situation better. (Send them a link to the video!)
At the same time, I wouldn't ever advise parents to sneak out the door just because they see their child is happy at play. Something as simple as a kiss on the forehead and, "Looks like you're having fun. I'll see you later," is all that's needed before they walk out the door. I've seen children have some pretty hard-to-calm breakdowns after realizing that a parent left without them knowing. It's a delicate balance between too much goodbye and not enough, but it's one worth finding.