There's nothing special about static methods, with regard to thread safety. If they access shared objects, then such access will usually need to be controlled by synchronisation; this might be on the object being accessed, some higher-level object or a special object allocated purely as a lock. The only way that you might think of them as special is that there's no instance of the Class on which you can synchronise. You can declare a static method as synchronised. If you do, it will be synchronised on the single Class object of the class in which it is declared. This means that only one thread can be executing any part of the method at any one time. However, I understand that the Java Runtime itself sometimes synchronises on this Class object for its own reasons, therefore you might sometimes find a synchronised static method blocks when no other thread is executing it. Usually better, therefore, to explicitly synchronise on some object or other, than to use synchronised static methods.
Betty Rubble? Well, I would go with Betty... but I'd be thinking of Wilma.