The reasons to leave this information off of your résumé are twofold. First is the old horse that we've been riding all across this list: Employers have to be careful about discrimination. The other reason is, why take a chance that your potential new boss really hates people with your political or religious views when you don't have to? It may be illegal for a company to discriminate based on politics, but good luck proving that the staunchly conservative human resources worker tossed your résumé in the trash because you listed your membership in the ACLU and Democratic Party, and not because you were genuinely unqualified for the job.
There are, again, some very narrow cases where not only is it fine for an employer to ask about your religion, but it might be to your benefit to do so. However, unless you're applying for a job as a priest or a nun, you probably don't have to worry about it too much.