A conscience clause is a legal loophole that lets you refuse to do part of your job if it violates your religious beliefs.
For example: Say you’re a pharmacist and your religion says birth control is wrong. If a rape victim approaches the counter and asks you to sell her a dose of emergency contraception, you are legally allowed to tell her to fuck off. You know, to put your conscience at ease.
The people who named the conscience clause want you to think conscience and religion are the same thing. Do you think they are? If you were a pharmacy manager, would you rest easy knowing employees you could not legally fire occasionally withheld medicine from people who needed it?
I wouldn’t want that on my conscience.