i think the reason they don't want to sing it is because they have to say, "I bow to thee, Mother." and in Islam u can't bow to anyone except allah so maybe that's why.
Many muslims bow and touch the feet of their parents and elders. In SRGMP Li'l Champs there is a contestant Sameer Mohammed and he touches Judges' (Bappi da, Alka, Abhijit) feet many times. If the clerics start interpreting everything according to religion, I am afraid the situation could turn explosive later on. Why is our *secular* media so silent now, everyone (in media) is saying that we shouldn't force anyone to sing it BUT to say that we WON'T sing it under any circumstances for whatever reason amounts to insulting our National Song. It unfortunately shows that for them their religious identity is more important than National Identity.