THIS TURNED INTO A RANT ABOUT THE BASIS OF MORALITY, AND WHAT'S MORE, IT'S A BIT OF ASS-PULL AND "JUST-SO" STORY TELLING. I COULD BE OFF-BASE COMPLETELY, WOO!
Anyway, the reason politicians need to have *some* religion to get elected, is because people still hold to the idea that you need to get your morals from some book, religion, or pulpit/priest, even if it's not their book. For them, morals just HAVE to be external, you can't trust your own judgement, they have to come from God!
Somehow, they never stop and think "Hey, maybe there's a reason that all these heathen religions have pretty much exactly the same morals as my religion..," or of the fact that almost every Christian does a pick-and-choose of the morals in the bible, and all the rest are "allegory" or "It was specific to the times, not a generalized rule!" despite that not actually being written into the book and for the most part, there's no real difference in context or concept for the morals in the book they follow versus the ones they don't. I.E. they're trusting their own judgement, and just think they're trusting the judgement of the book/priest.
Maybe, instead of coming from some God or written into the books as a novel idea, it's because most if not all the hard-core morals like "Don't steal, don't kill, respect [your elders]/[good people]/[respecting people being a good thing go do in general], stick with your tribe, help your fellow people, follow the Golden Rule of "Do unto others as you would have done to you", etc." are fairly ingrained into human beings, such as a genetic level? And the religions just codified them into rules, piggy-backing on things people generally already knew and accepted. So someone who doesn't believe in a religion would still have the same core of gut-instinct morality.
And the other morals, the ones that differ on a cultural basis like how you treat homosexuals (Abrahamic versus Greek versus Native American, for example), or certain animals being unclean, or how you treat your elders, depend on situational-to-the-culture factors. Such as nomadic cultures abandoning the elderly if they cannot make the yearly migration: No sedentary culture would do that, and it horrifies us, because our elderly are venerated or at least cared for because they helped with teaching the children and a long life-span of survival knowledge and cultural knowledge (Obviously before the last 200 years with the advent of medical science and centralized, professional healthcare, if you survive to 70 years old you must know SOMETHING to keep you alive). We don't have great hurdles that are make-or-break you that the elderly MUST participate in, so we don't need to cut them off like nomadic herdsmen do if they cannot survive the hurdle. (You don't often see the elderly in the fields, farming, for the same reason: They don't NEED to do the work (unless it's been a particularly rough time) so they aren't forced to, and are instead preserved for the aforementioned reasons)
Same for the others, religiously impure animals because those animals were literally unclean: It could hurt you to eat them, like the pig.