The new just makes it absolutely clear that you know you are stomping over an existing method. Since the existing code was protected, it isn’t as big a deal – you can safely add the new to stop it moaning.
The difference comes when your method does something different; any variable that references the derived class and calls Foo() would do something different (even with the same object) as one that references the base class and calls Foo():
SomeDerived obj = new SomeDerived();
obj.Foo(); // runs the new code
SomeBase objBase = obj; // still the same object
objBase.Foo(); // runs the old code
This could obviously have an impact on any existing code that knows about SomeDerived and calls Foo() – i.e. it is now running a completely different method.
Also, note that you could mark it protected internal, and use [InternalsVisibleTo] to provide access to your unit test (this is the most common use of [InternalsVisibleTo]; then your unit-tests can access it directly without the derived class.