I was recently playing around with Google and decided on a whim to use its business search to find out how many places near where I live teach martial arts. I knew there were a few, a nearby one even has a half off enrollment for spring deal going on, but I was really surprised at how many there are near me. According to a local newspaper's business search using the limit of 10 miles from my residence, the result was 38 places that teach martial arts (there are more since it doesn't count all martial arts as martial arts e.g. boxing, wrestling, etc. and that site does not list everyone - Google had some closer than 10 miles that were not on that list).
The reason I bring this up, beyond pointing out the surprising number of martial arts places nearby, is because of the Ranma fanon that Nerima is a martial arts Mecca. Considering that martial arts are a major part of the manga this view is not entirely unwarranted. The thing is there is not much to support that view point, only about a dozen martial arts show up and don't or didn't live there. The average person is not a martial artist and a dozen martial artists are not a lot; a typical class at a dojo would have more students than that.
Some people have pointed out the fact that the schools in the Ranmaverse sponsor various martial arts. This is not an unusual practice; it would be unusual if they didn't. Real life schools in Japan and elsewhere have school sponsored martial arts. Japan has been teaching martial arts in schools for a long time; just about every high school would have a Kendo club and some other type of martial arts after school activity. Even in the USA schools will often have martial arts. For example: wrestling, self defense classes, and archery.
The Ranma manga has quite a few made up martial arts, the thing is many of them are plausible and some of the ones people commonly think of as being made up actually do exist (though not in the way portrayed in the manga). Martial arts gymnastics exists in real life, just not in that form, and from what I heard it is becoming popular in California. Martial arts cheer leading exists as well, some martial arts places teach both cheer leading and martial arts and decided to combine the two (this should not come to a surprise considering that there are shows based on martial arts cheerleaders - see Kim Possible and Buffy the Vampire Slayer and a baton is just a staff weapon). Martial arts calligraphy and martial arts tea ceremony do not exist, as far as I know, but both are taught in a very similar manner to martial arts (have kata, master levels, training halls are called dojo, both were influenced by Zen Buddhism, etc.). Ukyo's martial arts style makes a lot of sense when you consider the ban on weapons Japan has. Improvising everyday items to be used as weapons is a common practice - for example Nguni stick fighters will often use any stick like object, such as an umbrella, to practice and fight with.
In real life there are thousands of martial arts, quite a few are as strange as or stranger than those seen in the Ranma manga. Capoeira is a martial arts dance. There are martial arts schools in Hong Kong that teach martial arts acting (combination Chinese Opera and martial arts to be used in films). Martial arts are interwoven into several religions (like Shinto and Buddhism but Christian martial arts exist as well). There are even martial arts styles that revolve on cheap shots and insults; a version of Shoalin Bushido has a kata that revolves around the use of verbal aggression, natural stances and sucker punches.