It seems that since Bruce Lee used them in his films in the early-70s, they increased in popularity and began to be banned in multiple countries. Wikipedia identifies Norway, Canada, Russia, Poland, Chile, Germany, England, Wales, Scotland and Spain as having strict regulations.
UK and German versions of Teenage Mutant Ninja Turtles (1990) had to be edited to remove Nunchaku (signature weapon for Michelangelo) from the film altogether.
Even looking at the other traditional Eastern fighting weapons used by the Ninja Turtles (Bo staff, sai, sword), I don't believe that any of them are as strictly regulated. Is there any reason for this? Are nunchaku particularly dangerous compared to other weapons used in martial arts? Were there a significant number of injuries at some point around the 70s-90s that led to these restrictions? Thanks!
I recall that they weren't even called Ninja Turtles here in Britain, they were the Teenage Mutant Hero Turtles.
You might be interested in this answer from u/TanukiPilot to "Why was the word Ninja censored in the U.K in the 80s and 90s?". It doesn't cover the full scope of your question but there is some reference to nunchucks.
Placing restrictions on personal weapons in civilian life is a complex topic but also fascinating. Many cultures in more distant history did so based on social class, for example after 1683 in Edo Period Japan, it was illegal for anyone wear Daisho (paired long and short sword) unless you were part of the samurai caste.
Restrictions created in the late 19th and much of 20th century, however, tended to have their roots in something that was fairly new at the time: rapid mass communication. This includes mass produced print media (books, newspapers, comics), radio, and later television and films. Mass communication meant that vivid stories and images could be widely disseminated, and also sensationalized. During these time periods, there were popular trends where specific weapons were featured either in crimes, or in crime fiction. Crimes where the weapon was somehow unusual often captured the popular imagination, even if statistically they were rather rare. A classic example is the blackjack during the early 20th century, documented in the excellent weapon history book Saps, Blackjacks and Slungshots by Robert Escobar. Blackjacks originally were general defense weapons used by gentleman (featured in R.G. Allanson-Winn's book on UK martial arts, although he derides them as inferior) and police officers, but acquired a reputation in the popular perception as deadly bludgeons used only by criminals as a result of several criminal cases as well as several pulp era comic books and radio plays. These depictions showed them as both sneaky and powerful, able to knock out with a single strike from behind (in real life, one single blow to the head rarely causes instant unconsciousness without just killing someone).
Nunchaku likewise really didn't start getting restricted until they started becoming popular in the public consciousness. The 1970s had them appearing both in films as well as several cases of crimes that, statistically speaking were pretty rare, but over-sensationalized in the media. The fact that they were both exotic "Eastern" weapons (I will not use the more rude term of the day) and relatively easy to craft from common materials only made things worse. Their effectiveness in fictional media gave them a reputation for power, which made them attractive to what I'll just call "knuckleheads," young foolish people who may or may not be criminally-inclined but have an unhealthy interest in combat, but not a lot of common sense or actual martial ability. This demographic would sometimes get in dust-ups on the street or engaging in some kind of petty non-violent crime and they would be found carrying nunchaku, leading to a popular impression that these were weapons for criminals. It is important to emphasize the latter, where the weapon is merely found in their possession, not actually used to commit violence. It's significantly more common, and might skew statistics, but actually doesn't support the assertion of that weapon being "more dangerous." This media-feeding-the-repulation phenomenon is not isolated to the United States, but happened across many countries, leading to these various bans being put in place.
In many parts of the United States, restrictions on these weapons have started to be reversed when challenged in the courts. One was Maloney v Singas, which struck down New York's 1974 ban. This case was especially illustrative regarding the history above, as it not only covered the history, but part of what fueled decision was the lack of evidence that nunchaku were used to actually harm people to any significant degree. To quote:
Furthermore, although the criminality associated with a weapon is not the only relevant inquiry here, there is virtually no evidence that nunchakus are associated with, or have been used to engage in, criminal conduct since Section 265.01(1) was amended to include nunchaku over forty years ago.