Yes, anime contact lenses are safe. It is safe whatever style lenses you wear. So it is safe to wear anime contact lenses as well. But you must keep in mind the rule:"don't sleep when you don't take off your eyes and keep your lenses clean." If you sleep with your contact lenses on, your eyes will not have enough rest and can't make air penetrate the eye. It will cause your eyes irritate and infect. Moreover, you should clean your contact lenses often with saline solution to keep it clean too.
Yes, they are safe to wear. However, wearing the contact lenses, whatever the type, may have the danger for the wearer if he or she doesn't have the hygiene habit. It is easily for the eyes to get infection. You should better not wear the contact lenses for more than eight hours a day. And you should put them in the contact lenses solution every day after you take them off.