This may surprise some. In my neighborhood in New York City (not in Brooklyn) the local mosque also broadcasts their calls to prayer over a loud speaker. I can hear it, and so can many of the Christians who live around me.
I can't really say why, but I've never been offended or worried. I guess it's just always seemed to me as part of their service. I would hope that if someone who walks by my church and hears our Christian music when we have the door open wouldn't be upset. I know it's not exactly the same -- we're not broadcasting our music on a loud speaker -- but it will do for now.
And to Meredith's question about carols being broadcast in the neighborhood: believe it or not, a neighborhood/shopping district near me actually does this. I meant to take a video and post it earlier, and I still may, but I was absolutely floored when I heard it. And they aren't just "holiday" carols -- they are full blown "Jesus is born" carols, belted over loud speakers attached to telephone polls.
Just thought I'd share my experience in a different New York neighborhood.