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 is His slave and Messenger.
Viewing a forbidden deed as permissible is called Istihlaal. The Istihlaal that takes a person out of the fold of Islam is that someone believes that a prohibited act is permissible, and also believes that prohibiting it is invalid and rejects its prohibition.
The case where Istihlaal becomes a reason for judging a person to be a disbeliever due to deeming a sin permissible is when this sin is prohibited based on the consensus of Muslims and its ruling is evidently known among them, like the prohibition of Zina (fornication). This case, however, is conditional on the absence of misconception or misinterpretation of texts. If there is any, then the person should not be judged as a disbeliever on account of his Istihlaal of the sin.
As for music and the like of it, deeming it permissible does not constitute an act of disbelief without any problematic aspects, since its prohibition is not decisive.
As for the person who discloses his sin or boasts about it and considers it “cool” as you expressed it, then such a person is upon a great danger and is subject to a severe threat of punishment. He might even be hindered from repentance. It is narrated on the authority of Abu Hurayrah that he heard the Messenger of Allah, sallallaahu ‘alayhi wa sallam, say: “All my followers will be forgiven except the Mujaahireen (those who commit a sin openly or disclose their sins to the people). An example of that is a man who commits a sin at night, and though Allah screens it from the people, he comes in the morning and says, ‘O so-and-so, I did such-and-such (a sin) yesterday.’ He spent his night screened by his Lord (none knowing about his sin), and in the morning, he removes Allah’s screen from himself.” [Al-Bukhari and Muslim]
Ibn Al-Qayyim said in Al-Jawaab Al-Kaafi: “A person boasts of his sin, and tells those who had no knowledge that he had committed it, saying: ‘O so-and-so, I committed such-and-such.’ Such a person will not be forgiven, and the road to repentance will be blocked before them, with all the doors leading to it closed for them in most cases.” [End of quote]
Al-Qurtubi said in Al-Mufhim: “This is one of the gravest major sins and worst acts of immorality. None would do this but someone who is unaware of the seriousness of the sin, or one who is taking it lightly and insistently committing it without intending to repent thereof while publicly disclosing his wrongdoing. A single act of these constitutes a major sin, so what would be the case if they are all combined?! That is the reason why the doer of these acts suffers the worst affliction in the worldly life and severest punishment in the Hereafter, as the punishments of all those acts are combined against him.” [End of quote]
Nonetheless, doing this does not necessitate that the doer is committing Istihlaal of a sin or denying that it is prohibited, and thus, he is not judged as a disbeliever merely for that.
We have not come across the context in which Ibn ‘Uthaymeen said the statement you cited. Perhaps he was referring to those who boast of the sin while taking the Greatness of The Creator lightly and belittling His Right.
Anyway, according to the affirmed scholarly principle regarding this issue, judging a person as a disbeliever is limited to incidents that involve neither ambiguity nor probability. In general, the words of Ibn ‘Uthaymeen imply a warning against taking sins lightly and considering them a source of pride and boastfulness, and that whoever does this is upon great danger.
Allah Knows best.