Some People in the United State Often Say Previous Generations Were More Chaste and Less Promiscuous than More Recent Generations. Does the Historical Record Support This?

I don't know how far in the past you want, but you might be interested in the Kinsey Reports. This was a huge 2 part study on human sexual activity in America led by Alfred Kinsey; one volume about men was published in 1948 and another volume about women was published in 1953 [Sexual Behavior in the Human Male and Sexual Behavior in the Human Female respectively.] Both involved a few 1000 participants, Kinsey and co. had long in depth interviews with each participant about sex

If you can access the reports themselves, you're in for an interesting read. There are about a zillion statistics on all kinds of sex. Ask a librarian. To make a long story short, people absolutely were sexually active, including in ways they weren't supposed to be. Some highlights as taken from my senior thesis, which included some stuff on Kinsey:

Most people are not exclusively homosexual or heterosexual [Male Kinsey report, p. 392; Female report, p. 466]
About 25% of married people [male or female] had committed adultery by age 40 [Sexual Behavior in the Human Male, 724; Sexual Behavior in the Human Female, 416]
a majority of men reported breaking the law on the way to an orgasm [can't currently find the page number for this fact but if anyone needs it I'll dig harder] Note that gay sex and certain other kinds of sex were illegal no matter how old the participants were or if they consented to sex
premarital sex was very common despite being taboo, premarital "petting" [making out] was nearly universal regardless of gender or other factors such as religion [each report has an entire chapter on this topic]

Both reports were easily accessible to the public and became best-sellers despite being essentially dry scientific literature. For my thesis I looked at a bunch of reviews and editorials about the report in newspapers from that time [via newspapers dot com].

The female report especially made waves; many people weren't happy to hear that women weren't living up to the sexual rules that existed for them. To sum up a great number of opinions I read:

Many people objected to the fact that anybody could read the Kinsey reports. They felt that, in uneducated hands, it would serve as a corrupting influence [i.e. an endorsement of the "wrong" sexual practices] or as nothing more than titillating reading material, cheapening the science
Some people insisted that the sample sizes were too small and/or that they must have included only the most sexually wanton part of the population; "surely not THAT many people are unfaithful to their spouses?!?"
Kinsey was otherwise known as an entomologist [bug expert] which some people used to discount his work; some suggested that someone like a psychoanalyst should have conducted this study instead of him
My very favorite newspaper report was from a person convinced that the reports would be the downfall of America and that Kinsey was "worse than both Hitler and Marx." Other editorials written in a similarly hysterical tone aren't too tough to find. [“Report is ‘Bunk Plus Arrogance,’” The Tablet (Brooklyn, NY), August 8, 1953]

One book that can give you a sense of the reception without reading a million papers like i did is An Analysis of the Kinsey Reports of Sexual Behavior in the Human Male and Female, ed. Donald Porter Geddes (New York: E.P. Dutton & Co., 1954).

My conclusion is that Kinsey's facts reflect the actual activities people were occupying themselves with, and the response reflects both a national interest in sex and a national interest in moral guardianship and repression.