We were on the Anthem in May and every night in the main dining room the head waiter gave my husband the next night's menu so he could pick what he wanted. They were very helpful. After the first night, our waiter had gluten free bread on the table without having to ask for it. In the back of the Windjammer there is a gluten free section.
It was also noted on our reservation that my husband was gluten free. The head waiter had a list of quite a few people with allergies and he spoke to all every night.