Curiously, go through spirit management for what? That the pilot was criticizing Gryder while on his own time, with his own opinion, and not representing Spirit nor speaking for them?
To harm said pilot, basically threaten their employment, by connecting their commentary with whatever...
Weirdly enough, "own time and own opinion" (i.e. 1st amendment stuff) does not trump "Major Airline Social Media Policy." So... it all depends on if there is a connection between your Social Account and your virtual airline. And totally up to the discretion of airline management if they want to open up a Section 19 about something you opined about online.
Sadly, in the world we live in, there is 'currency' in your # of followers.
In a nutshell, as it stands today, you don't have any speech rights if your employer deems that they were harmed by your online speech, IAW the "social media policy." The 1st amendment is protection from the state stopping you from saying whatever you want... not from saying anything you want if there is any connection between your online presence and your employer. (That is, within the current interpretations of 1A.)
Our resident curmudgeon Richman might be able to file the serial #'s off some of the issues he's dealt with and give some more color about exactly how this works. There are definitely shades of gray when someone threatens to go to your employer with screenshots, recordings, whatever.
A good policy to follow is not to say anything online that you don't want to see and defend on an 80in. screen - either in the CP's office, dicipline hearing, or court of law.