The Mexican helper was named "Hey Soos". The actual spelling of his name is "Jesus", which, in Spanish, is pronounced "hey soos". There would have been letters of outrage if the character was named "Jesus".
Despite Gil Favor and his men being on several cattle drives, the majority are clean-shaven, which would be difficult and dangerous without access to clean water. It was also rare at the time for men to be clean-shaven when working around livestock.