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.
It looks like what you need is not to prevent the execution of your dependent tests but to report the results of your unit test in a more structured way that allows you to identify when an error in a test cascades onto other failed tests.