Controller tests throw "No route matches" exception when routing throw a Rack application

I’m migrating various static routes to a wildcard route that points to a custom Rack application – very similar to this

Now the tests for the affected ActionController::TestCase’s throw ActionController::UrlGenerationError: No route matches exceptions. Is there some way to prevent the controller tests from checking existing routes or is there some other preferred way to test my controllers in this case? Switching to ActionDispatch::IntegrationTest’s would be one possibility.