In mainstream Orthodox Jewish practice, men do not listen to females outside their immediate family sing. This restriction has recently been tested, with the Israeli army insisting all soldiers attend non-entertainment ceremonies in which women sing, although leaving individual exemptions up to commanding officers. The reaction among Israeli rabbis varied.
Like in many areas of Jewish law, authorities have historically debated the parameters of this prohibition and minority views have allowed for exceptions. My impression based on media reports is that the majority of rabbis who consider army service a great mitzvah allow for leniency if necessary. When soldiers have no other option, they may attend events with women singers rather than face military disciplinary measures, especially if it contributes to unit cohesion. See here for reports of permissive rulings, albeit somewhat different, by R. Yuval Cherlow and R. Shlomo Aviner: link. And here for the IDF Chief Rabbi’s: link. According to this report, R. Mosheh Lichtenstein seems to allow for leniency in other situations as well: link (Hebrew).
This is not a new question. Religious soldiers have been serving in the Israeli Defense Forces since its inception. I believe it is worthwhile to examine how halakhic authorities have addressed this issue in the past. I did not find anything relevant in the IDF Rabbinate’s guides available online: link. However, two guides for soldiers written by instructors at mainstream Hesder yeshivas offer explicit instruction.
R. Yosef Tzvi Rimon, of Yeshivat Har Etzion, in his guidebook for religious soldiers, Tzava Ka-Halakhah, 2007 edition p. 324, 2010 edition p. 261:
שירת חיילות: יש מקום לדון בעניין זה באריכות ואכמ״ל, אבל נציין שלכתחילה צריך להקפיד שלא תהיה שירה של חיילות, וצריך לבקש להיעדר מהופעות של להקות צבאיות שיש בהן בנות. כאשר אנו נאלצים להיות במקום כזה, צריך להקפיד שלא להסתכל בפניה של החיילת השרה, ורצוי לשיר ביחד איתה (כי כששרים, לא פנויים כל כך לשמוע).
The singing of female soldiers: There is room to discuss this matter at length but this is not the place. However, we will note that we should preferably ensure that there will not be any singing of female soldiers. You must ask to be excused from performances of military bands that include women. When you are forced to be in such a situation, you have to be careful not to look at the face of the female soldier who is singing and you should preferably sing along with her (because when we sing, we are not as able to listen).
R. Zechariah Ben Shlomo, formerly of Yeshivat Sha’alvim, in his Hilkhos Tzava (1986, 2001), pp. 28-29:
כאמור לעיל סעיף א, אסור לשמוע קול שיר של אשה, ועל אחת כמה וכמה שירי עגבים וכיו״ב. לכן, אסור לשמוע מקהלות של נשים, וצריך לדאוג מראש שלא להשתתף באירועים הכוללים שירה של זמרת או זמרות או תערובת זמרים וזמרות, וכ״כ הצגות וכיו״ב השייכים למושג המורחב היום של ״תרבות״.
The added implications of the recent controversy may cause these rabbis to change their rulings. However, absent the press and the pressure, this is how they ruled on this delicate matter of law and sensitivity.
As we said in paragraph A, it is forbidden to listen to a woman’s singing voice and even moreso love songs and the like. Therefore, it is forbidden to listen to women’s choirs. And you have to take care in advance to avoid participating in events that include singing of a woman or women or a mixture of men and women. And similarly plays and the like that are part of the broad contemporary concept of “culture”.