I think that your best bet would be to find historical examples where blind obedience resulted in horrific realities. For instance, discussing those who silently collaborated or followed orders of the Nazis might be a great start. Schlink's work, "The Reader," might be a very good start, as well. Another literary resource that resonates with a historical discussion would be Jackson's short story, "The Lottery." Additionally, Miller's drama, "The Crucible," would be another instance where one can see the results of following tradition and not offering questioning to its practices. In each of these works and in identifying historical settings such as Nazism, or other examples of individuals following practices like segregation or discrimination without offering questions or opposition, one can see that the following of tradition in a blind or purely obedient stance results in terrible consequences. In this light, one can provide a justification against tradition being followed blindly. The premise of the question is a philosophical one because I see it as asking how individuals should act and what they should do. Yet, I find that the basis for beginning to address it can rest in historical justification.
Nothing should be followed blindly. Taking the literal meaning of the phrase, even blind people use means other than sight to reduce the problems of acting blindly.
Tradition is a useful starting point for guiding current action. Tradition represents what has been found to be consistently right and useful in the past and, therefor, has been adopted by many people as a standard practice. But times change and, with that, requirements change. As a result, traditions can and do become outdated. It is important to note that traditions are not static. These do change with the changing times. Only problems is that average people, often lack either the intelligence to see the need for change, or the courage to take risk of venturing in the uncharted waters of breaking traditions.
Also there may be situations where traditions are still useful in general, but exceptions to tradition is justified because of some special circumstances or requirements. When we act blindly we fail to see the signs pointing to the need for changing the traditions or deviating from them.