The following contains non-plot related spoilers for Fantastic Beasts: The Crimes of Grindelwald.
If you were part of the lucky generation that grew up with the Harry Potter books or the films that came with them, then the series worked perfectly. The eight movies came out over the course of a decade, so a young child who is perfectly fine seeing Harry Potter and the Sorcerer's Stone in the theaters is also the right age for seeing something like the much darker Harry Potter and the Deathly Hallows many years later. The franchise matured over the years, and while the early films were safe for most ages, the later movies were clearly for an older set. So where does Fantastic Beasts: The Crimes of Grindelwald fit in? While not quite as grim as the latter Harry Potter films, it also not as light and breezy as the early ones.
While my own daughter is still too young to watch movies of any kind, I am very much looking forward to the day we can start sharing film together, and so I've begun watching all movies with an eye toward what will be acceptable, and when. The Harry Potter franchise will be a special set of films someday, and if she really loves them, we can watch the Fantastic Beasts movies too because there's really nothing here that will be inappropriate for a kid who has seen the rest of the franchise.
To be sure, Fantastic Beasts: The Crimes of Grindelwald is a film for the older Harry Potter fan, but that has more to do with the film's tone and pacing than any potentially objectionable content found within.
When it comes to your big three content warnings, language, sex and violence, you can write off the first two pretty much entirely. Nobody uses any language that I noticed that wouldn't be acceptable when speaking with your grandmother, and most of the film's relationships are so dysfunctional that nothing resembling romance even makes it on screen, much less anything more passionate. Perhaps romantic entanglements will become a bigger deal in later parts of the series, but not here.
When it comes to violence, the story is a little bit different, but not by much. If you've seen any of the Harry Potter franchise, then the sort of violence will be familiar to you. It's almost all done via magic wand, which makes it pretty bloodless and disconnected from reality. Attention is drawn to the spectacle of the magic rather than what's being done with it.
There are a couple of exceptions. People do die in the movie, and in every case where it's a nameless side character (i.e. not anybody the audience will be attached to), most of whom are killed offscreen, there is still attention drawn to it. In an early sequence, Grindelwald sets up a base of operations by having the people who live there killed. Their bodies are removed in coffins and placed in a hearse sitting outside for the purpose. The most potentially disturbing moment comes when the villains discover a child still alive in the house. What happens to him occurs off-screen, but there's no question as to his fate. Another sequence, which might be too intense for some, deals with the death of an infant, although these scenes might actually be a bigger issue for the parents in the audience than their kids.
Another nameless character is killed via magic, on-screen, near the end, but it's not even made perfectly clear that the person is dead. They just fall to the ground after being hit with a blast of magical energy.
While the subtitle of the film is The Crimes of Grindelwald, and thus the bulk of the plot focuses on the villain played by Johnny Depp and his master plan, the film doesn't forget the Fantastic Beasts part of its name. There are a few new interesting creatures that appear, as well as some returning favorites from the previous film. These are by far the best moments in the film and the ones most likely to entertain any viewers on the younger side. The magical effects are visually stunning as always. The creatures are cute, or spooky, or otherwise interesting to look at, and it just makes you wish there were more of it.
Ultimately, the thing that might not make Fantastic Beasts: The Crimes of Grindelwald acceptable for some kids is going to be the overall tone of the movie. It's a dark and serious movie overall, and the film certainly takes its time. It's over two hours long and the pacing is not particularly fast, which has the potential to cause younger kids (also older kids and adults) to simply get bored with this movie while they're waiting for the next magical creature to arrive.
If you or your kids are serious Potter-heads and steeped in the lore, then the movie may be highly interesting. If not, however, the rapid-fire way that names and relationships are fired off, especially at the end, may leave some viewers, of any age, potentially confused.
Part of what the made the Harry Potter films interesting to kids was the fact that the main characters were kids themselves. It made the story easy to relate to. That's just not an option here. The characters here are not unrelatable, just less so. Eddie Redmayne's Newt Scamander may be particularly relatable to some children due to his own difficulty connecting to others on screen, something many in the audience may struggle with especially at a young age.
The story of this movie isn't mature in the sense that it's inappropriate for children, I'm just not sure it will interest them. Everybody's kids are different, and so not every child, even of the same age, will react to Fantastic Beasts: The Crimes of Grindelwald in quite the same way. There really isn't much in the movie that I would expect most parents would object to their children seeing. The bigger question is simply whether or not your kids will actually enjoy the film.