How safe is the soap children are using to wash their hands to kill infectious diseases and bacteria?

It depends on the soap dispenser.

According to a recent study, nearly 25 percent of the soap from open, refillable bulk soap dispensers in schools is contaminated with bacteria. In addition, the research found that washing with soap from bulk dispensers left 10 times as much bacteria on student's hands than if washed with soap from sealed dispensing systems, such as a cartridge or bag.

The study also suggests that contaminated bulk soap may contribute to cross-contamination in schools as bacteria is transferred from hands to surfaces. And, soap in bulk dispensers becomes contaminated because it's exposed to bacteria from janitors' hands, toilet water that plumes out of the bowl after flushing, and dust in the air.