The Rambam writes (Hilchos Lulav 8:14): [The Simchas Beis Hashoeva on Succos] "was not celebrated by ignoramuses or by anyone who wanted, but by gedolei chachmei Yisroel and Roshei Hayeshivos and the Sanhedrin and the Chassidim and the elders and men of good deeds. These were the people who danced and clapped and played [the music] and rejoiced in the Mikdosh during the festival of Succos. But all of the people came to see and to listen."
We learn from this that seeing and hearing a simcha shel mitzvah means to see and hear the simchah of gedolei Yisroel and the chassidim and elders that is all kedushoh, and this arouses a spirit of holiness that comes from a simcha shel mitzvah.
And from this we should understand how careful we must be to avoid the opposite of this, that is, to see and listen to the music of reshoim even at a simcha shel mitzvah. But we must make sure that the whole execution of the simchah should be from a holy source, and even if they change slightly the words or the music, tumah should not be acquired by changing it to kedushah, and we should distance ourselves from these songs.
The hosts of simchos must request and make conditions with the musicians that they play only songs and tunes from holy sources and not chas vesholom the opposite.
May it be that we will merit speedily to an everlasting simcha from the building of the Beis Hamikdash,
(The letter was also signed by HaRav Shmuel Halevi Wosner, and HaRav Chaim Pinchas Scheinberg.)The letter isn't exactly on point here. The issue as Dei'ah V'dibbur explains it is not just the use of secular songs, but even Jewish music that is composed or played in a secular style. Rav Karelitz's letter, on the other hand, only addresses the use of secular songs, which generally isn't such a big problem at simchos. I've posted previously here and here about the plagiarism of secular songs in Jewish music, but few of these songs are typically played at affairs. The ones that are are Yidden, Asher Bara (Piamenta), and Turkish Kiss (also Piamenta), other than that the pop/rock music played at a typical "frum" affair is the various classic rock riffs (i.e. Cream's Sunshine of Your Love, Deep Purple's "Smoke on the Water, the Rolling Stones "Jumping Jack Flash") that are often played during "Keitzad Merakdin", and the fanfare for the chosson and kallah which frequently is a riff or theme from a pop tune like Gerry Rafferty's "Baker Street" or Europe's "Final Countdown." In other words, the problem of secular songs is one that is much smaller than the (alleged) problem of secular influences.