I have noticed two behaviours that are becoming more acceptable in modern orthodox circles and was wondering whether it had just become something people do or whether there was a halachic basis for allowing it. 1) Men hearing women singing live at a concert or a musical. 2) Religious women performing for a mixed crowd. Many thanks for your thoughts on this.

Shalom, I cannot comment as to whether this has become more acceptable or common, but halachically there are those who are lenient if a number of women are singing together. Some are lenient if the is heard through a microphone and not directly. Some are lenient since today women singing is common and men are less likely to be aroused by this. Some are lenient that the prohibition is to say verses or prayers when women are singing but not to just hear them. These are reasons that have been suggested why some are lenient, but it is preferable to observe the halacha to the highest standards when possible, Kol Tuv