I had the exact same problem and thought. It all came about a couple of updates ago and kids could simply go into their message app and select a GIF or a sticker and they could search just about any word and pull up a GIF. Yes some of them are terrible. Here's the fix:
First, make sure you have restrictions turned on and they need to ask for permission before downloading any apps.
Second, follow this link
http://help.apple.com/iphone/10/#/iphf9c9c01d3
Delete the GIF app from the "managed" section and your child won't be able to access those pictures any more. Hope this helps.