Explanation
In the United States, refusing food offered by a host is generally acceptable if done politely, especially if you have a dietary restriction or are full. However, in family settings, a direct refusal without explanation can be seen as slightly rude or unappreciative, so it's better to offer a brief, honest reason or accept a small portion.
Local Tip
If you must refuse, say 'No thank you, I'm full but it looks delicious' or 'I have an allergy' to show appreciation without offending.
How it compares elsewhere
Refusing food offered by a host is often considered impolite; it's better to accept a small amount even if you don't eat it.
Refusing food, especially in a family setting, can be seen as rejecting hospitality; a polite 'I'm full' may still lead to insistence.
Refusing food is acceptable if you explain politely, but refusing a homemade dish may be taken as a slight to the cook's effort.