By who? When and where?
Why wouldn't they want to see a pilot gain experience they don't have in an airplane almost everyone has- that also further qualifies you for a good job? it shows you are pro-active and trying to keep your learning curve steep in a time of stagnation.
You have to understand- some view SWA as the best job going- most other airlines view themselves as better or equal-and saw's elite position is a very relative new development-
a direct quote from a recruiter to me: "if we don't pay enough to retain a pilot we'd like to keep, then that's a great argument to mgmt for our contract" the other side- mgmt would like to see every pilot they have on first year pay- if you leave, they replace you with a cheaper pilot.
Whether it's flight ops or mgmt recruiters, no one has much of a reason to discriminate against you for having the type- just the opposite actually- it's the pilots that leave after a few months of getting a 737 type through continental, delta, or AAA that costs them. If you already have the type- that's not a concern now.
Now will you have to explain it? Absolutely- be ready to show why you want to work where you are applying over anyone else, including SWA- but as a stand alone issue- I have never seen what you are saying prove out. Just pilots making stuff up. So show me something to make it credible-
I know Alaska used to, and maybe still do- but it's a pretty insecure company to be that silly.