All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
Your question is good and deserves attention and answer. Yes, it is true that whoever reads the beginning of the question might find it somewhat strange, but the intended meaning becomes clear upon reading the question in full.
Feeling annoyed and distressed when witnessing or hearing sinful actions is something commendable, and it is an indication of goodness and evidence of Eemaan (faith). It is the duty of a believer to display protective jealousy when one of the sacred ordinances of Allah, The Almighty, is violated. Muhammad ibn ‘Ali ibn Al-Husayn, may Allaah have mercy upon him, said: “Prophet Ibraaheem (Abraham) was protectively jealous, and the person who is not protectively jealous is none but someone whose heart is turned upside down (faith cannot settle within it).”
However, one should not settle for such protective jealousy and being annoyed only; rather, it is incumbent on a Muslim to forbid such evils to the best of his ability. It has been narrated that Abu Sa‘eed Al-Khudri said: “I heard the Messenger of Allah, sallallaahu ‘alayhi wa sallam, say: ‘Whoever among you sees an evil, let him change it by his hand (physically). If he cannot do that, then by his tongue (by speaking out). If he cannot do that, then by his heart (by hating it and disapproving of it), and that is the weakest form of faith.’” [Muslim]
There is no doubt that there are Muslims who do not denounce what they see of sinful acts, even if only by their hearts, like non-adherence to Hijaab and listening to music. Rather, they may even respond to them with prohibited gazing and listening. This is proof of indifference and weakness of faith as they do not denounce sin by their hearts, let alone changing them by their hands or tongues. Such people are in great danger, as Allah, The Exalted, Says (what means): {Cursed were those who disbelieved among the Children of Israel by the tongue of David and of Jesus, the son of Mary. That was because they disobeyed and [habitually] transgressed. They used not to prevent one another from wrongdoing that they did. How wretched was that which they were doing.} [Quran 5:78-79]
It is important to note that it is wrong to make a generalization that Muslims do not experience such feelings that you have mentioned, as there are many Muslims who are good and protectively jealous with regard to their religion.
Allah knows best.