the vest does indeed block X-Rays. they do it when you're at the dentist so the images captured wont show your chest bones. The shit they make you put in your mouth, thats so your jaw bone and other teeth dont show, or the back of your skull.
If you're getting an arm/leg Xrayed you dont need a vest cause the can position the camera so that they dont need to block other bones from showing on the image.
About going to the moon, We go in space ships that are designed to block radiation from people inside. same with space suits.