They may not be able to discriminate based on religious beliefs but they most definitely can and will discriminate based on qualifications. Like most jobs, nursing is very competitive so if they find another nurse who is better suited for the job, then you will be poop out of luck. If you checked "yes", that means you've met that requirement are are prepared to give blood, but if you checked "no", they have every right to question your competencies and if you don't have any, they will choose someone who does. It's simple economics. Hopefully, you wouldn't lie about it and not fully disclose the truth because that would be unprofessional and unethical and, as you well know, we nurses are nothing if not professional and ethical.
Not as troublesome? So you believe that in an emergency life or death situation religious preferences should trump attempting to save a human life? That's an absolute scary thought and sure as heck wouldn't hold up in a court of law.
Your post was very biased which is not surprising, but luckily several others have chimed in on the other side of the equation, certainly the OP will benefit from hearing about all angles of this dilemma and not just the fluffy perfect world interpretation.