1st Amendment, free exercise clause.
If you really believe that forcing a person to commit an act their religion regards as murder isn’t a state violation of free exercise, one wonders what you wouldn’t tolerate. We don’t even force people to kill the enemy in a war, for Pete’s sake.
I don't think anyone is saying the guy can't be Catholic or whatever but rather that pharmacies must carry certain drugs to be licensed and if you can't accept the licensing restrictions, find some other line of work. People who object on religious basis to some government policy or other must support them with their taxes or go to jail. That's not an establishment of religion either.