What easily available bar soap is least likely to cause breakouts on your back & shoulders?

Neutragena. There are many excellent bar soaps, even the moisturizing ones such as dove, are non comedogenic. Don't scrub your back if there are pimples as that can create a more inflammatory acne.
Lever 2000. Lever 2000 has antibacterial properties and does not cause allergies. Safeguard is irritating for some people and benzoyl peroxide cause irritation in about 5 per cent of people who use it.
Panoxyl, lever 2000. Lever 200 is a non irritating soap with antibacterial properties that can possibly help. You can also lamisil, (terbinafine) a soap containing benzoyl peroxide to decrease breakouts. 5 per cent are sensitive to benzoyl peroxide.