When the TV ratings first came out in 1996, it was a pretty good way to gauge how adult shows seemed in the past. If a show from the 1960s or 1970s was rated TV-PG in the late 1990s, there was a good shot that it was considered geared for adults during its original run. Monty Python and M*A*S*H were examples of shows that were regularly rated TV-PG in reruns. TOS was a show that would sometimes be rated TV-G and sometimes be rated TV-PG. That put it just slightly less adult than the Star Trek shows of the Berman-era, or the sitcoms on Must See TV, most of which were rated TV-PG (though Seinfeld would have an occasional TV-G episode). The first episode of Star Trek rated TV-14 was Carpenter Street, on ENT, which aired in 2003. To compare the movies, TMP was rated G, but rerated PG for more intense effects with the Director's Edition. First Contact was the first PG-13 movie, Insurrection was PG again, and all the movies since have been PG-13.
TOS was designed to be a show that wasn't necessarily for adults, but was more serious and realistic than the shows designed for children's matinee serials of the previous generation. The aesthetic was supposed to evoke the US Navy, Air Force, and NASA, and have a utilitarian look, as opposed to the Googie look of much of the rest of science fiction of the time.
But, I think my advice to parents who want family-friendly Star Trek is that, like Doctor Who (which started out designed as an educational children's show with a science-fiction coat of paint, has had spinoffs aimed at a very adult audience with Torchwood, and younger audiences like K-9 and the Sarah Jane Adventures), the franchise is so prolific, that it's possible to curate based on interest level and age appropriateness, and still have a vast amount of content. If you start a kid on Trek at six, maybe you'd pick the lighter episodes of TOS, TAS, TNG, VOY, and maybe the PG-rated movies, most of which can be viewed out of order. By the time they get to late elementary school, they'd be ready for some of the tougher material in all of those series, the rest of the movies, and ENT. Then follow that up with the more nuanced DS9 and DSC when they get to middle school and high school. I know for me, by accident of age, I started Trek with TNG season four, when I was in fourth grade, and DS9 was perfectly timed for me, starting in sixth grade and ending the day before I graduated high school.
I think there was a great description of what the content added in this SPOILERY comment from
page-3.
Oh, and if present-day sailors swear, then I'm kind of shocked 22nd-24th century space sailors don't swear nearly as much.