If a pump-based soap is a necessity, options do exist. Unlike many of the other liquid soaps available, Dr. Bronner's new formulations of its Shikakai line of pump soaps contain no preservatives of any kind, and no synthetic detergents.
Shikakai is a seed pod from a South Asian tree and (similar to soap nuts) has been used as a cleanser for centuries.
Dr. Bronner's uses their castile soap base and mixes in shikakai from organic sugar and grape juice.
The 12-ounce bottle is not inexpensive, is mild, and lasts for ages. Available in lavender, peppermint, tea trea, lemon-grass lime, and a formula for babies. (Dr. Bronner's Magic Skikakai Soap, 12 oz. bottle $8.99)