I finally heard back from the rangers at the Grand Canyon. From their perspective, hammocks are OKAY! Here are the details:
You are more than welcome to bring your hammock for camping at Mather. The
only restriction is that if you are not physically at your site you must
take it down, such as run to the store or to the showers or out for the
day. We have had issues where the deer and elk get tangled up in them.
Supervisor Visitor Use Assistant
Grand Canyon National Park