There is a reason why people are so skittish about fecal matter, and that is because the stuff is downright filthy.
Our solid waste is packed with bacteria that house everything from mild stomach bugs to serious infectious epidemics.
This is why the invention of indoor plumbing and the widespread adoption of bathroom sanitation (hand washing, disinfecting, etc.) is the best method of reducing the spread of bacterial illnesses around the world.
A bidet cleans like a shower does, with a pressurised stream of water, theoretically washing away more fecal matter than one could with endless wipes of dry paper.
Though few studies have been done on the effectiveness of bidets in societal hygiene, anyone who uses one will tell you that the personal difference in cleanliness is dramatic.