I find myself (surprisingly, considering how often we disagree) siding to a large degree with WIY here.
One might be able to make an argument that there is SOME non Jewish music that is not objectionable and unlikely to have a negative effect on the Jewish soul.
One might also be able to make the separate argument that, say, instrumental music is inherently spiritual and without words to taint it can be uplifting.
One could even go so far as to look for and find heterim, leniencies, or personal justifications for listening to non Jewish music even with words. I can think of many songs with positive messages – but not necessarily Jewish ones.
But none of these ascribes positive Jewish attributes and outcomes to this music. Josh Groban singing about J but using Tanach verses to do so isn’t uplifting, its as depressing as combating a missionary doing the same thing, only Groban is doing it for money and the missionary is doing it for neshamos.
Lets not make an idol out of Groban just because he shaves and wears a suit instead of showing off bling and tattoos. At the end of the day it IS a particularly important time of year to have a particularly Jewish perspective on how life should be lived.
For the past 10 years I’ve been spending RH and YK in a very small town with a tiny mostly non religious Jewish community as their baal tefiloh and baal koreh and mechazek. They get little enough Yiddishkeit in their lives, it is sometimes the simple Jewish tunes I use in davening that make a huge impression of memory and tradition on them that I can then expand when I give a vort or a shiur.
I am a big proponent of taking what is good and useful from chochmas hagoyim, and even to a lesser extent, their culture. But that doesn’t mean we have to give it a mantle of holiness, even if we can get our heads around giving it a chezkas kashrus.