and the words on the label you need to be aware of are "disinfectant" and "antibacterial," the latter being especially silly because plain soap made with a fat and an alkali is antibacterial. However, those two labels signify things in the soap you might not want for everyday use.
Most people who are concerned about chemicals in soap are concerned about parabens, which are used as preservatives, especially important in high oil soaps. While a few people get contact dermatitis from them (it's rare), there are no data about long term exposure. That work is being done now. If you're concerned about those, search "paraben free soap/shampoo." Amazon alone has several pages of them.
These products also don't contain sodium laureth ether sulfate, a scary looking chemical detergent derived mostly from coconut oil. That one is in all large commercial brands of soap, shampoo, body wash, toothpaste, and many cosmetics. The research is in on that one, it is safe. There was a scandal a couple of decades ago about contamination with dioxane, a byproduct of its manufacture, but a level of 300ppm or less is considered safe.
My own bugaboo is fragrance, it breaks me out like crazy and "natural lavender" is one of the worst. I cling to Dr. Bronner's peppermint and fragrance free laundry soap. I can cope with the scary sounding chemicals, but nix on the hearts and flowers, thanks.