Although the word airhead is found in every edition of The American Heritage Dictionary, the pejorative sense of the word only entered the lexicon with the third edition, which has a copyright date of 1992. The second college edition, from 1982 and the first edition of the book only have the word in its militaristic sense as an Arial territory secured by paratroopers. I also checked the 1980 Oxord American Dictionary, and it lacks the word altogether. This is important for several reasons:
The first importance is that because the 1990s were at the end of the 20th century, it represented the culmination of all social changes made in the century beforehand. This concept was put into words in the ubiquitous catchphrase "It's the '90s!", which served as a reminder that we lived in less old-fashioned times, generally intending to imply that things have progressed considerably, if not unfathomably. One reason somebody might exclaim "C'mon, it's the 90s!" is to disabuse somebody of any obsolescent sexist notions, since that was something we were trying hard to avoid. (Another reason would be to try and excuse actions that would be considered airheaded by conventional wisdom.)
I even have a copy of what is presumably (the copyright page is torn out of it) the 1991 Random House Webster's College Dictionary and that has a two page appendix entitled "Avoiding Sexist Language", which the June 11th, 1991 New York Times article Nonsexist Dictionary Spells Out Rudeness by Richard Bernstein describes. I doubt such a ubiquitous pejorative could be effectively inducted into the popular vocabulary during that time, if it was perceived as specifically misogynistic, since that is precisely the sort of language we were trying so hard to avoid then. It would not make sense for this word to be one of the more unreserved insults of that time. The year 1994 seemed to especially like it. Consider the following quote:
"Although 'Beavis and Butt-head' satirizes psychobabble and political correctness, the show is mostly an airhead exercise in aimless activity." — The New Yorker, Volume 70, issues 1-6 - Page 97
There was even a movie called Airheads in 1994 (which a now deleted answer exemplified here first,) and all of the star role idiots were male too. Yeah, it is probably not going to be called the greatest movie that was ever made anytime soon, but you would think with an 11 million dollar budget, that they would have afforded to at least double check if the title was applicable.
The second and more relevant importance is that it helps give me a period to find establishing non-feminine uses of this meaning, as it was understood prior to any bias established by the dictionaries. My Random House Webster College Dictionary further gives me a date of origination between 1975 and 1980. Consider the following quotations from that period:
"Case 3–3: You know, it says here in this labor history book that Terrence. V. Powderly wanted a shorter workday for —get this— extra time for workers to compose sonnets — you know, the 14 lines of rhyming iambic pentameter stuff. Can you believe that? What an airhead! "If he had succeeded, we would really be messed up today," said Bubba Bristol." — Union-management Relations in a Changing Economy by Alan Balfour, page 66 1987
Sometimes people tell you directly that you aren't very smart, but most of the time they ignore your attempts to display your intelligence, or they kid about you being a "space case" or an "airhead." After a while you are bound to see yourself as not very intelligent, particularly if the people who have been sending you those messages aboutyourself are important to you. — Speaking with Confidence and Skill By Lynne Kelly, Arden K. Watson 1989
"'He was going for those Reagan Democrats,' Joe continues explaining. 'Except there aren't any Reagan Democrats, there're just cut-and-dried rednecks. Now that I'm down south here, I understand better what it's all about. It's all about blacks. One hundred thirty years after Abe Lincoln, the Republicans have got the anti-black vote and it's bigger than any Democratic Presidential candidate can cope with, barring a massive depression or a boo-boo the size of Watergate. Ollie North doesn't do it. Reagan being an airhead didn't do it. Face it: the bulk of this country is scared to death of the blacks. That's the one gut issue we've got.'" — Rabbit at Rest, a fictional novel by John Updike, 1990
"'He's an airhead, Regan is', the man said at the backyard barbecue at a home near Santa Monica near the ocean where the smog is not so bad. 'I thought only women could be airheads,' a woman remarked about this newest bit of slang out of the television industry 'women are bimbos,' the first speaker explained in didactic tones, 'Anybody can be an airhead and I still can't believe that that airhead is going to live in the Whitehouse.' 'He's not an airhead, he's a smoghead and he is going to live in the white house,' said another. The guests laughed and/or moaned, for this was a gathering of liberal Californians who regard Regan as a personal affliction, as though he were a judgement and a punishment for their 'lifestyle', to use the state's favourite neologism." — The first paragraph of "Moral Hypocrisy on The Right" by Nicholas von Hoffman in the October 18th 1980 issue of The Spectator, page 9
So if the claim "anybody can be an airhead" is correct, which is a more-or-less agreeable assertion to me, why are all of those synonyms feminine? Well, the first thing to consider is that synonyms are only rarely if ever perfect. Wiktionary is proposing those words as a synonym for "silly person" yet each of those words have their own nuances. I'm almost surprised "clown" and "goofball" aren't on the list.
The second is that dictionaries are bad at conveying nuances, especially the modern ones which strive for inclusiveness rather than depth of coverage. An airhead is not really just any old fool, but a particular kind. I shall not bore you with the details here, since this is not a question of precise nuances. Some connotations are necessary though, and the easiest to exemplify here are "silly" in the A.H.D. and "scatterbrained" from Random House's. With those two words in mind, there is a close synonym for airhead:
slang chiefly US a silly scatterbrained person
[C20: back-formation from ditzy] — Collins English Dictionary – Complete and Unabridged, 12th Edition
This synonym is in fact so close, that Random House's entry for it just refers back to the airhead entry in both their 1991 and 2010 dictionaries. There is something that Collins is not telling us about the word though, which the Cambridge Advanced Learner's Dictionary & Thesaurus does:
a ditzy person, especially a woman, is silly:
She played the role of a ditzy blonde.
Keep in mind that "especially" means "usually" rather than "only" in the lexicography biz. Nevertheless, there is a point here. These and other mental traits of the airhead are more often considered feminine than masculine. This makes it a closer match to those more feminine words than other generic insults, and besides that it gives some people the false impression that the word is gendered as it is much more often applied to females and in some uses, strongly implied a female. Applicability is a separate consideration from actual application though, and as the word airhead did not have any bodily requisites by the time it was established as a part of the popular vocabulary, I would ultimately deign it a gender neutral word. However, it can still have sexist implications. Consider a quote like this for instance:
"I don't believe for one second you haven't squawked to Bennett or that blond airhead I'm trying to bang." — Little Saigon by T. Jefferson Parker, 1989, page 340
Despite nothing being expressly said, I would be surprised if that "blond Airhead" was not a woman, with the word airhead being used as a euphemism for bimbo, in the same way "bang" is being used as a euphemism for … Well, actually it would be inaccurate to say "bang" is being used as a euphemism per-se, because some rather foul language does occur in the source material. However in defense of the neutrality of the actual word, there are also contexts where I would suppose the opposite:
"I should have known better than to let the mechanic Binkley work on my car. That airhead misadjusted the valves." — Making it Explicit by Robert B. Brandom 1994, page 311
I wish I could see the fuller context, since it seems to make extensive use of the example. Also of note is that Google alleges this quotation be found in The Philosopher's Annual Volume 7 by Roeman and Littlefield, 1986, but it won't give me enough of a page preview to completely affirm that.
In closure, I would like to make just one more quote to reiterate the main point. "Bart seems like such an airhead, but he’s all heart." Now that sounds like something you might hear on The Simpsons, but I got it from the 2006 "McGraw-Hill's Dictionary of American Slang and Colloquial Expressions".