Question: I'm wondering if there is a test framework that allows for tests to be declared as being dependent on other tests. This would imply that they should not be run, or that their results should not be prominently displayed, if the tests that they depend on do not pass.

The point of such a setup would be to allow the root cause to be more readily determined in a situation where there are many test failures.

As a bonus, it would be great if there some way to use an object created with one test as a fixture for other tests.

Is this feature set provided by any of the Python testing frameworks? Or would such an approach be antithetical to unit testing's underlying philosophy?

Answer: 
> 
> Or would such an approach be
>  antithetical to unit testing's
>  underlying philosophy?
> 
> 
> 

Yep...if it is a unit test, it should be able to run on its own. Anytime I have found someone wanting to create dependencies on tests was due to the code being structured in a poor manner. I am not saying this is the instance in your case but it can often be a sign of code smell.
This seems to be a recurring question - e.g. #3396055

It most probably isn't a unit-test, because they should be fast (and independent). So running them all isn't a big drag. I can see where this might help in short-circuiting integration/regression runs to save time. If this is a major need for you, I'd tag the setup tests with [Core] or some such attribute.

I then proceed to write a build script which has two tasks 

* Taskn : run all tests in X,Y,Z dlls marked with tag [Core]
* Taskn+1 depends on Taskn: run all tests in X,Y,Z dlls excluding those marked with tag [Core]

(Taskn+1 shouldn't run if Taskn didn't succeed.) It isn't a perfect solution - e.g. it would just bail out if any one [Core] test failed. But I guess you should be fixing the Core ones instead of proceeding with Non-Core tests.