The original wording of the 2nd Amendment, as written by Madison, included a conscientious objector clause. There is only one reason for that. Because it was written in the context of military (militia) service. Some of the reference to militia service is still there.
When the phrasing of all the Amendments was considered and modified, for some reason the Senate committee removed that portion. At that time, the Senate did not retain records of their proceedings like the House did, so nobody knows why.