As of 2019.1.4 build 735, custom render textures on avatars stop updating when you open the avatar, social, or safety menus.
This is related to the issue https://vrchat.canny.io/bug-reports/p/custom-render-textures-bugged-on-avatars where CRTs stop updating after switching worlds, but is a new issue that makes CRTs pretty unusable on avatars at the moment since there is no decent way to restore the update on CRTs once they stop.