What kind of action could be perceived as a reproach?

Being in disagree with a fact, comment or statement and expressing it is a reproach.

Explanation:

Depending on the context and ocassion, you can use the best approach to make your position clear, if you are using the wrong words and tone it can be interpreted as a reproach, if you use a more polite approaching and be clear your argument can be received as a suggestion, comment or reproach.

Protesting against a certain law could be considered as an example of "reproaching" because reproaching is when you express dissatisfaction or disapproval.