While digging for an article about the woman kicked off the JetBlue flight this year for wearing the burlesque shorts I found this story Here’s Why JetBlue Can Legally Kick You Off a Plane for Wearing Booty Shorts which has in it:
So what gives Southwest, JetBlue, or any other airline the right to
boot you off a flight? It comes down to the “contract of carriage,” a
legal document that spells out the rights and responsibilities of the
airline and its passengers. Whether you realize it or not, you agree
to that contract whenever you purchase a ticket from an airline. In
JetBlue’s case, it states that the airline can refuse “persons whose
conduct is or has been known to be disorderly, abusive, offensive,
threatening, intimidating violent, or whose clothing is lewd, obscene,
or patently offensive.” Most other carriers use very similar language.
The story links to the JetBlue Contract of Carriage but as per the quote Southwest will have a similar contract.
So the answer to your question is yes - they can kick you off the flight. But I am guessing that you would't even make it to the gate wearing a mankini.
OK .. found the Southwest Contract of Carriage
Acceptance of Passengers
a. Refusal to Transport
(8) Comfort and Safety.
General. Carrier may, in its sole discretion, refuse to transport,
or may remove from an aircraft at any point, any Passenger in any of
the circumstances listed below....
(i) Persons whose conduct is or has been known to be disorderly, abusive,
offensive, threatening, intimidating, violent, or whose clothing is
lewd, obscene, or patently offensive.
(ii) Persons who are barefoot and older than five years of age, unless required due to a disability.
So you could be refused to fly under paras 6 a. (8) (i) and (ii) (the latter if you are not wearing shoes which I don't think Borat(?) did - but that's my assumption!)
Now the fun legal question is if you can be bound by a "contract" that you didn't know existed!