What is the religious ruling on killing two small, immature sparrows by throwing their nest into the street due to an unwillingness to have them on the balcony?

There is no sin upon you as long as you did not intentionally take the lives of those birds, for Allah, the Almighty, says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful." Sin is only incurred by one who intentionally commits falsehood.