The "conscience clause" itself doesn't mention religion it only mentions conscience. People are allowed to make their own decisions whether they are religious or not. (You don't even need Dawkins to tell you what to believe.)
Emergency Hormonal Contraception is sold by pharmacists to prevent pregnancy after unprotected sex but a similar drug could be used to force abortion of a fetus.
I've pinched this next bit from another forum from a similar thread.
"Abort a fetus a week or so before it's due to be born anyway – murder probably.
Abort a fetus at a time when it probably wouldn't be able to live – murder perhaps.
Abort a fetus well before it could possibly survive – killing something human.
Abort an emplanted embrio – disruption of the creation of a human being.
Prevent the emplantation of an embrio – prevent the creation of a (already defined) new human being.
Prevent sperm and egg from fusing (e.g. condom, condemned by the Catholic church remember) – prevent the creation of a unique human being.
Prevent donors of egg and sperm from enabling them to fuse (e.g. two people on opposite sides of the world are not allowed to meet) – prevent circumstances in which a human embrio could be created.
Where do you draw the line?"
At some point you have to make a decision based on your own conscience.