The taboo is when you only test in production. At the very least you should manually try out your app after deploying a change. As far as automated integration

The taboo is when you only test in production. At the very least you should manually try out your app after deploying a change. As far as automated integration tests in production, it is simple as identifying which tests are prod safe, and marking them. That really depends on the app, but in a web app it generally means all the GET requests, plus some of the others.