Is it good practice to let abstract classes define instance variables?
public abstract class ExternalScript extends Script {
String source;
public
Sure.. Why not?
Abstract base classes are just a convenience to house behavior and data common to 2 or more classes in a single place for efficiency of storage and maintenance. Its an implementation detail.
Take care however that you are not using an abstract base class where you should be using an interface. Refer to Interface vs Base class