I think Olin is overlooking something important, however. My sense is that peremptory challenges exist in the United States because juries have to be unanimous, at least in most jurisdictions. In a criminal case, every single juror has to agree for the jury to convict or acquit; a single juror can hang a jury and avoid either a conviction or acquittal. When a single juror can control the outcome of a case, it is reasonable to give parties the power to screen out jurors who they see (whether rightly or wrongly) as unrepresentative of the community at large. Peremptories can filter out unrepresentative viewpoints and leave a more accurate picture of core community values and attitudes.
The Amish, who shun judging others under their faith, would be excused from jury service on religious reasons under a bill sent to Governor Bob Taft for a signature......So the idea is to create a legal right to avoid jury duty for a special segment of the population who have a certain set of religious beliefs that the government has decided are deserving of protection not given to any other religious beliefs. (Paging the establishment clause! Establishment clause, please call your office...)
Disclaimer The opinions expressed herein are my own personal opinions and do not represent my employer's view in anyway.