Colleen, Please tell your customers what the rules are and then enforce them - with the goodwill and humor that is unique to Southwest. Even restaurants post "No shoes - No Shirt - No Service" signs.
But, as a long time Southwest customer, I don't want to be confronted (and never have been) by flight crews enforcing their own opinions. That would be contrary to the style that has made Southwest successful, and could infest Southwest flight crews with the dominatrix mentality present on other airlines. (Many of us have experienced the "Go ahead and argue with me, and I'll slap your butt in jail" attitude, but not on Southwest.)
Finally, to passengers who are easily offended, get over it. Your dress code does not apply to others. The only rules that apply are those imposed by the airline. If that doesn't suit you, you can always drive to your destination and your rules will apply!
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