If a Michalel Shabbos turns on the radio on Shabbos may you listen to the radio? The Shevet HaKehosi (5:57) brings from the Ravi Pesach Frank (Har Tzvi 1:183) that it is a difficult question and it is hard to be Matir. Especially if it causes a Chillul Hashem and it lends support to Chillul Shabbos and the person who was Michalel Shabbos.However says the Shevet HaKehosi, it is permissible to hear the news from a person who listened to a radio on Shabbos. He compares this to the Heter of the Maharshag (1:43) who says that although if someone turns on the lights on Shabbos it is assur to do anything in the room that you could not have done with the lights off, nevertheless if someone prepared food in the room, after the lights were turned on, you may eat the food. He explains that the Chachomim only made it Assur to enjoy the light itself and not things that benefited from the light.
Similarly since you are only hearing the news from someone who heard it from the radio and not from the radio itself it is permissible.