What are the necessities that permit the declaration of one's nakedness (or private parts), such as Abu Bakr's saying, "Suck on the clitoris of Al-Lat," and to what extent does this apply to contemporary situations like obscene statements made in response to injustice?

The necessities that permit such speech cannot be enumerated, but examples can be given to serve as a measure. Estimating necessity requires knowledge, piety, trustworthiness, and preservation, so that the exception does not become the rule. The situation mentioned in the question is not indicated by religious law, nor is it palatable to good taste, nor is it approved by reason. Therefore, closing this door entirely is better than expanding it without a legitimate religious excuse.