Is he who deems permissible musical instruments not accompanied by haram (forbidden acts) due to whims and lust, and insists on their permissibility, an infidel? And how sound is the attribution of deeming permissible musical instruments as an act of disbelief to Ibn Taymiyyah?

This issue (musical instruments) is not among the issues that entail disbelief (takfir). A group of the best Muslim scholars held this view, even though it is a weak opinion. Whoever follows this opinion out of personal desire and caprice is mistaken, but the issue is not one that leads to takfir. There is no text from Shaykh al-Islam in which he declares the one who considers musical instruments permissible to be a disbeliever, and it seems that he does not hold that view, as he affirms the difference of opinion on the matter and explains that it is a weak difference, and that the opinion of permissibility is an outlier. Moreover, Shaykh al-Islam is among the furthest people from takfir.