This 2015 study, Bactericidal effects of triclosan in soap both in vitro and in vivo, suggests the most popular active ingredient, triclosan, had no effect for exposures commensurate with hand-washing:
There was no significant difference (P > 0.05) in bactericidal activity between plain soap and antibacterial soap at either test temperature. However, antibacterial soap showed significantly greater bactericidal effects after 9 h. These results suggest that although triclosan-containing soap does have antibacterial activity, the effects are not apparent during the short time required for hand washing.
Antibacterial soap containing triclosan (0.3%) was no more effective than plain soap at reducing bacterial contamination when used under 'real-life' conditions. The present study provides practical information that may prove useful for both industry and governments.