If a song is written by a Yid but is recorded with a non-Jewish singer, is there an issue listening to it? Is the concept of connecting to his Neshama apply here as well?
It is not forbidden to listen to a non-Jew sing. This is provided that the music, either the lyrics or the purpose of the music, is consistent with Torah, i.e. it’s not heretical, immodest, or goes against other Jewish values.
This is purely from a halachic point of view. However, in other sources, the concept connecting to the soul of the composer of non-Jewish music is discussed. This applies specifically to the composer and not to the singer or the one playing. Albeit, there is room for one who wishes to be stringent in this matter and listen to only a Jew singing or playing.
At the same token, if the singer is singing verses of Tanach or mentioning G-d there could be concern that his intentions are for Avoda Zara and thus it would be forbidden to listen to such a singer unless verified that their thoughts are truly pure.
See Likkutei Dibburim 1, Likkut 4, Sicha of 20 Kislev 5694 ch. 5: “When one sings a song composed by another, one unites with his Chayah-Yechidah”. See also Toras Menachem 5747 II p. 647 about non-Jewish lullabies. See also Hachsharas Ha’avreichim 9 (from the Piasetzner Rebbe). See at length Responsa Vayeshev Hayam (Hillel) 2:7.
Note however that in Imrei Sha’ul, Inyanei Zimrah V’simcha 41 from the Modzitzer Rebbe, he quotes in the name of his grandfather from Zvolin, that a person is taking a major responsibility upon himself when he makes song heard because the elevation of the soul and its descent are dependent on music. “It all depends on the musician, what he is playing and how he is playing it.”
See a similar point in Likutei Maharan 1:3.
מִי שֶׁשּׁוֹמֵעַ נְגִינָה מִמְּנַגֵּן רָשָׁע קָשֶׁה לוֹ לַעֲבוֹדַת הַבּוֹרֵא. וּכְשֶׁשּׁוֹמֵעַ מִמְּנַגֵּן כָּשֵׁר וְהָגוּן, אֲזַי טוֹב לוֹ … מִי שֶׁהוּא כָּשֵׁר נִמְשֶׁכֶת הַנְּגִינָה שֶׁלּוֹ מִן הַשְּׁתֵּי צִפֳּרִים חַיּוֹת טְהוֹרוֹת … וּכְשֶׁהַמְּנַגֵּן הוּא רָשָׁע אֲזַי הוּא לוֹקֵחַ הַנְּגִינָה שֶׁלּוֹ מִצִּפֳּרִים אֲחֵרוֹת שֶׁבִּקְּלִפָּה.
It should be noted that when the servants of King Shaul sought out a musician, they looked specifically for one who had good character traits (Shmuel 1:16:18): And one of the youths called out and said, “I have seen a son of Yishai from Beis Lechem who knows how to play music, is of great strength, of profound understanding, a man of stature, and Hashem is with him.”
See Shulchan Aruch Admur Hazaken (Orach Chayim 338:3) where from there one can see that in the past non-Jews would some times play music at a Chuppah that went into Friday night-Shabbos. This deals with the issue purely a halachic point of view and refers to playing music, not singing, and it deals specifically with a case when a Jew is not available (because it is Shabbos). Obviously, where a Jew is available one must always rather employ a Jew, in all employment.
See also Igros Moshe Yoreh Deah 2:56 who writes that it is forbidden to listen to a non-Jew singing verses of Psalms for it is almost certain that their thoughts are to their deities. Based on the Gemarah in Chagigah 15, it can bring to מינות and transgresses a Biblical commandment of לא ישמע על פיך.