The Peking Duck has a good post offering an explanation and debate (read the comments) on that sign from Fists of Fury. The content of one actual existing sign from 1917 in Shanghai, as shown in photos at the duck, was less provocative but similarly intentioned.:

PUBLIC AND RESERVE GARDENS.
REGULATIONS.
1. The gardens are reserved for the foreign community.
2. The Gardens are open daily to the public from 6 a.m. and will be closed half an hour after midnight.
3. No persons are admitted unless respectably dressed.
4. Dogs and bicycles are not admitted.
(continues…)

ESNW, meanwhile, looks at similar signs in China and Asia.:

"Notice: All unauthorized Chinese and dogs are not permitted to enter, or else you are responsible for all the consequences.  May 1".  This unsigned notice was written with a chalk pen on a small blackboard hung on the gate of a factory on Yuannan Street in Lihuan District.  When the reporter went there yesterday, the old factory building appears to be empty with no sign of production activities.  On the outside were two stone tablets which said "Guanzhou Bicycle Axel Cover Factory" and "Guangzhou City Wuyang Bicycle Enterprises Sports Equipment Factory."