This seems like your typical fighter pilot/inter service rivalry humor. Could be about either the F/A-18 or about the Navy, and if the former, it's been around for a long time. Some of the earliest examples I can think of come from when the Bug was new on the block, and they and the Turkey communities would make jokes and innuendos about each other; long history there between fighter and attack squadrons, and it wouldn't surprise me if the Intruder folks were involved as well. As it was explained to me by the Fighter side, and this was a few years ago so I'm not going to get it exactly right, you had your Fighter Guys and your Attack Guys. When the Bug showed up, you had Fighter Attack Guys. Spell that as an acronym, and that's the joke - it would come off as something like "The Bug's a neat little plane with the Fly By Wire controls, air to air and air to ground weapons and all. But if I wanted to fly one I'd have to become a FAG." Yes, it is homophobic. It was also still among jokes executed when the F-14's were retiring - in the last Fighter Fling movie (2004) there is a cutaway joke where a voice over asks "What else is on" - the channel changes from 14 to 15 to 16 to 17 to 18. On Channel 18 is a rendition of the introduction of "Queer Eye for the Straight Guy" but with F/A-18 squadron patches flying around making a bunch of changes. The voice says something along the lines of "This sucks, change it back to 14." and the video continues. Ironic, now that the F/A-18 has taken over for the F-14, and some of the guys making those jokes have become Fighter Attack Guys (and Gals).
Now, I'm not sure if the picture above is a shoot on the Bug or on the Navy, considering there is an F-16 it may be the latter. I hear jokes like this about the Navy from the USAF side to this day, though it's fairly uncommon where I've been stationed and usually comes from some old-hat. They aren't right in any way, by any stretch of the imagination, but they are something you'll run into even if you look back less than 10 years.
EDIT: Come to think of it, just such a joke was originally in the script for TOP GUN the movie. An earlier rendition had this happen in the club:
"NEARBY - AN A7 pilot stands by the bar. He knows Goose and speaks loudly for his benefit.. A7 PILOT You know the Fighter Pilots motto? It's better to be dead than to look bad. They grin broadly. Goose replies as they brush past. GOOSE I don't know, Frank, anybody gets off on bombing the shit out of dirt has got to be queer. Goose exchanges friendly punches with the attack pilots. "
Not right, but common.