The reason why cats eat moths is mainly because they think moths are a nutritious food. In addition, cats may be attracted by the moth's activities, thus preying on them.
Cats are very curious about many creatures, especially this flying insect, who will pounce on them and grab them and try to eat them. This is the instinct determined by genes. Cats will also eat some insects and flying insects in the natural environment. Moths are just one of them, and they will not have any adverse effects when eaten.
You can always pay attention to the changes in the cat and send it to the pet hospital in time if there are adverse reactions. If you are really worried, you can use vomiting method to spit out the moths you eat from the cat.