Are the twisted, ropey strands of egg white safe?
Yes. These strands are the chalazae which anchor the yolk in the center of the thick white. They’re composed of nutritious egg albumen and do not indicate contamination. In fact, the more prominent the chalazae, the fresher the egg. These natural parts of the egg don’t interfere with cooking or beating of the white and you don’t need to remove them, although some cooks like to strain them from stirred custard.