As a Captain for Southwest Airlines Company, maybe I can clear up some of this...
Most US Airlines (Majors) don't require any TPIC. Southwest requires a minimum of 1000 TPIC. However, the successful applicants generally have many times the minima.
In addition, SWA requires the new hire to come to class already typed on the 737 (lowers our insurance to have both pilots typed).
While SWA has about a 50-50 Military/Civilian pilot group make up, we hire pilots from all backgrounds. I have flown with pilots that flew crop dusters and some who flew the Space Shuttle, and all types in between. We hire for personality, and train for proficiency.
As a side note: I don't recommend the Shuttle type entry into LAX, but I have seen it done.