In the film Clerks (1994)Dante and his girlfriend have a fight about sexual partners.
She says she has only had 3 while it later comes out that she has had oral sex with 37. She maintains that oral sex is only "fooling around" and not actual sex.
During the hearings about the Clinton-Lewinsky scandal in 1998 Bill Clinton famously denied having a sexual relationship with Monica Lewinsky. When it came out that they had oral sex on multiple occasions he also defended it by saying oral sex is not sex, just "fooling around".
Was this a common cultural attitude at the time?
It was a common cultural attitude in the sense that we have evidence from the 1990s suggesting many people did not consider oral sex to count as "having sex."
In 1999, the Journal of the American Medical Assocation published an article by Stephanie A. Sanders and June Machover Reinisch (both of the Kinsey Institute) entitled "Would You Say You 'Had Sex' If . . . ?" The article was based on a survey taken among students at a major Midwestern state university campus in 1991 as part of the university's efforts to gain information on student sexual behavior in order to assess community sexual health and sexually transmitted disease transmission risk. As part of the survey, respondents were asked, "Would you say you 'had sex' with someone if the most intimate behavior you engaged in was . . ." followed by a variety of possibilities. The number who answered affirmatively--meaning they would consider the behavior to constitute "had sex"--was the following:
The responses were also broken down by the respondents' genders. Male respondents were more likely to consider nearly all types of contact to be "had sex" except for the last two, where they were slightly less likely. The respondents were from many states, were nearly all heterosexual, were majority sexually experienced, and the authors particularly noted were mostly self-identified as moderate to conservative and included more registered Republicans than Democrats. Very few of the respondents were over 30.
So the survey demonstrated that, at least on one college campus, counting oral-genital contact as "had sex" was a minority position.
By the way, publication of this article in 1999 was very controversial and led to the forced resignation of the journal's editor (who had allowed the article to be published), on the grounds that JAMA as a medical journal should not have published an article on a political topic. (The public health significance of this type of findings, I think I should point, is significant: if you are trying to assess the sexual activity and health of a population and plan to ask, "Have you had sex?" then you need to know that some 60 percent don't count oral sex and 20 percent don't count anal sex. That means you should probably frame it differently.)
Of course, surveys of college students don't really tell us about cultural attitudes outside this population. I am not aware of robust studies that would tell us whether heterosexual American adults in general considered oral sex as "had sex" at this time.
There was a somewhat later moral panic over teenagers engaging in rampant oral sex, but I would locate that as occurring in 2004-06 and thus being subject to the 20-year rule.
EDIT to fix a broken sentence and confirm this is the same article linked by u/You-Are-Number-Six.
A brief report published in January 1999 in JAMA (the Journal of the American Medical Association) essentially asked this question. Written at the time of the impeachment process, the opening line is 'The current public debate regarding whether oral sex constitutes having "had sex" or sexual relations...'
The authors looked at data from a survey of around 600 US students from 29 states conducted in 1991 (so before the Clinton affair could have altered their view) which showed 59% did not consider oral sex as having "had sex."
The paper should be free to access and is quite short: https://jamanetwork.com/journals/jama/fullarticle/188367
Sex education has always been controversial in America, but the 90s is where we saw the first major fracture in the program.
The first was the formal adoption and funding of abstinence only education, as signed by then-president Clinton in the welfare reform act. This meant that public schools could be permitted to adopt a sex education curriculum that had a thesis of "no sex" is the best protection.
The second was the global HIV/AIDS epidemic that brought about increased visibility of STDs. Here's short history from planned Parenthood that chronicles this. The inclusion of HIV/AIDs education became something of a springboard for renewed discussion of STDs as a part of sex-ed, which until that point had focused primarily sexual development and pregnancy.
The pamphlet cites several sources that highlight the multi decade struggle for "comprehensive" sexual education, which (insofar as I can tell) is not adopted at the federal level, meaning that states still have a wide range of sex-ed course material that may or may not include oral sex.
I could go on but ultimately I'm trying to prove a negative here. It's hard to find state-based materials from the 90s, skim them, and confirm if they do or do not include content about oral sex. Between the cultural references you've made and the material I've found so far from the 90s decade there's a notional conclusion that oral sex was something of an "other" that wasn't strictly defined in any of these materials as overtly a "sex act".