Are there any cultural customs I should be careful not to offend?
The people of Curaçao are very accepting and are not easily offended by tourist behavior as long as you remain friendly and respectful. For example, two men or two women walking hand in hand is a relatively normal sight in Curaçao, especially in downtown Willemstad.
In religious places it's considered respectful to keep your voice down, and wearing a kippah is required in the synagogue. Also, when visiting a store, supermarket, or restaurant, it's considered bad form to come in only a bathing suit, and you may be denied service.