Why can final object be modified?

final just means the reference can't be changed. You can't reassign INSTANCE to another reference if it's declared as final. The internal state of the object is still mutable.

final ConfigurationService INSTANCE = new ConfigurationService();
ConfigurationService anotherInstance = new ConfigurationService();
INSTANCE = anotherInstance;

would throw a compilation error

The key to the misunderstanding is in your question's title. It's not the object which is final, it's the variable. The variable's value can't change, but the data within it can.

Always remember that when you declare a reference type variable, the value of that variable is a reference, not an object.

final simply makes the object reference unchangeable. The object it points to is not immutable by doing this. INSTANCE can never refer to another object, but the object it refers to may change state.

Being final is not the same as being immutable.

final != immutable

The final keyword is used to make sure the reference is not changed ( that is, the reference it has can't be substituted with a new one )

But, if the attribute is self is modifiable it is ok to do what you have just described.

For instance

class SomeHighLevelClass {
    public final MutableObject someFinalObject = new MutableObject();
}

If we instantiate this class, we won't be able to assign other value to the the attribute someFinalObject because it is final.

So this is not possible:

....
SomeHighLevelClass someObject = new SomeHighLevelClass();
MutableObject impostor  = new MutableObject();
someObject.someFinal = impostor; // not allowed because someFinal is .. well final

But if the object it self is mutable like this:

class MutableObject {
     private int n = 0;

     public void incrementNumber() {
         n++;
     }
     public String toString(){
         return ""+n;
     }
}  

Then, the value contained by that mutable object may be changed.

SomeHighLevelClass someObject = new SomeHighLevelClass();

someObject.someFinal.incrementNumber();
someObject.someFinal.incrementNumber();
someObject.someFinal.incrementNumber();

System.out.println( someObject.someFinal ); // prints 3

This has the same effect that your post:

public static void addProvider(ConfigurationProvider provider) {
    INSTANCE.providers.add(provider);
}

Here you are not changing the value of INSTANCE, your are modifying its internal state ( via, providers.add method )

if you want to prevent that the class definition should be changed like this:

public final class ConfigurationService {
    private static final ConfigurationService INSTANCE = new ConfigurationService();
    private List providers;

    private ConfigurationService() {
        providers = new ArrayList();
    }
    // Avoid modifications      
    //public static void addProvider(ConfigurationProvider provider) {
    //    INSTANCE.providers.add(provider);
    //}
    // No mutators allowed anymore :) 
....

But, it might not make much sense :)

By the way, you also have to synchronize access to it basically for the same reason.