And lack of propriety,
And quite a variety
Of unpleasant names.
But it's not against any religion
To want to dispose of a pigeon.
Well, it doesn't seem to be against any of the Abrahamic religions. If anything, the reduction of animal suffering is the furthest thing from the religious text's agendas. If anything, increase of suffering for animals seems to be the goal (in order to clean the sins of others). Although the following line is "So if Sunday you're free" -- which would count as work on the Sabbath for some Christian faiths, though much of those faiths ignore most of the commandments so there's not much of an objection there. Judaism still holds the Sabbath on the 7th day ("For in six days the Lord made the heavens and the earth, the sea, and all that is in them, and rested on the seventh day; therefore the Lord blessed the Sabbath day, and hallowed it" -- Which makes the Christian switch to the first day seem a little less hallowed). And that isn't the specific claim. The specific claim is killing the pigeons not the day of work.
However, there are rather obvious objections to killing pigeons within Jainism and wanting to kill pigeons within Buddhism. It is strictly speaking against at least one religion "to want to dispose of a pigeon" -- I have nothing against the slaughter of birds but I can't stand inaccurate song lyrics!