Static utility methods are not so bad. You can hide a package-private strategy behind the static call. This can be easily tested (and replaced) given that the test case belongs to the same package. Moreover, it makes the code very readable. Of course, the clients of the static utility method can still only use one implementation in their tests. So here is some inflexibility.
Bohemian is right when talking about state. If your static utilities have state you are doing something wrong.
About your question: If you want to avoid static methods you can use the spring framework and define different implementations of utilities that you use and test in different contexts. In this case, however, access to these objects is not so convenient as you must first obtain a reference to the context that knows your utility object.
