If the mic wasn't on we wouldn't be able to discuss the mic being on?
What are you not getting?
Below 10,000 feet, the only allowable conversation is safety of flight.
Clearly a stuck mic is safety of flight. So are flaps, gear, selection of speed, altitude, or communication about the airplane energy state, runway, ILS frequency, or any other topic having to do with flying that airplane at that moment.
Discussing what people drive, or your feelings about the city, is clearly not safety of flight.
The mic is used to transmit over the radio, not to talk with each other.
When a radio is transmitting, reception is blocked. So, when you are holding down the transmit button, either intentionally, or inadvertently, you cannot hear any other transmission, including a transmission from the tower saying, “stuck mike”.
In some airplanes, loud ones like the 737, pilots use an intercom to speak to each other. The radio side tone sounds a lot like the intercom. I’m quite certain that this pilot did not know he was transmitting.
Again, it’s not what was said, it’s when it was said. His statement was said below 10,000 feet when extraneous speech is prohibited for safety reasons.
As far as job implications, an employer can fire a pilot for any action that brings discredit to the airline. The First Amendment protects an American citizen from government action, but if do something that makes Southwest Airlines look bad, while wearing a Southwest uniform, and while flying a Southwest airplane, they have every right to terminate you. Your right to freedom of expression is intact, but you have violated the terms of your employment.
Pilots have in the past have faced disciplinary action, up to and including termination, for failing to realize that. Social media posts have gotten pilots in trouble recently. Both ALPA and major airlines have had to remind pilots of their contractual constraints.
If you wish to post a controversial opinion on social media, you may do so as a pilot, as long as your profile does not link you to your profession. If you’ve got a picture of you in a company uniform, on the flight deck of a company airplane, as part of your profile, then, yes, you had better be careful not to bring discredit upon yourself or your employer.