When you work with short-lived feature branches, feature toggles help you sleep at night by quarantining new code for partially implemented features. Yet, there may still be a worry that somehow there was some lapse in feature toggle implementation and side-effects have crept in.
Automated tests add one more layer of security. Automated tests cover both unit tests (associated with TDD) and integration/acceptance tests (associated with BDD). When you are confident that your code has good unit test coverage and integration test coverage, you have sound reason to believe that feature toggles are correctly quarantining new code.
Automated tests should be run by developers before merging code to the master branch. In addition, a solid continuous integration process will run the full suite of automated tests and reject the merge if any tests do not pass. (Note: You should run automated tests with various configurations of feature toggles to simulate the settings for each environment - test, staging, and production.)