Remember those old commercials for Resse's Peanut Butter Cups, where they one person would say "Get your chocolate out of my peanut butter" and the other person would come back with "Get your peanut butter off of my chocolate!" Then they would taste the two together and confectionery bliss: achieved!
In a typical week, I lift weights, teach a yoga class, and attend two Judo classes, a Zumba and a Belly Dance class. I occasionally (When I can make time and have the energy reserves) Put on a suit of armor and hit my friends with sticks, hopefully more often than I get hit. The point is, I subject myself to a wide range of kinds of movement that I'm not always familiar with. I enjoy the challenge, I enjoy the people, and the movements themselves are pretty fun to execute.
If you hang out in the martial arts pond long enough, or the yoga one, and I suspect the dance one as well, you start to find people and products that seek to blend one or more disciplines together. Some of these make a lot of sense, (Yoga and pilates are a good combo!). But others are weird hodgepodges that don't improve either thing they combine.
For example, in the medieval fighting I do, people from the dance world will often try to contribute to the fighting world by teaching fighters to dance. Some go as far as to construct a "fighter's dance". And it's pretty cool, as long as you don't want to get better at fighting.
Training specificity is a thing. However, sometimes there is carryover!
For example, I have discovered that my sense of timing has improved in my Judo and Sword fighting practices, owing to my Bellydance teacher's insistence that I follow the beat, and match my motions to it. Zumba has taught me to be lighter on my feet. Yoga has vastly improved my mind game. Weight lifting has made me strong, so I can train longer, and also hit hard, even when I'm not in ideal conditions.
Now don't get me wrong. If you are tenth degree blackbelt, with years of teaching and practicing, feel free to create a Dance infused karate style! The problem comes when relatively inexperienced folks start combing arts together, without regard for the intended application of those arts.
So, Go practice your Judo, or Karate. Go rock out to your Zumba Class. Go Shimmy your hips and belly to your hearts content. But do it primarily because you love it! The other bennies will come in time. And They'll come out of YOUR body's synthesizing facility, which is WAY better than someone's product!