Hip hop has influenced Japanese culture to some degree. Samurai Champloo (released in 2004) is the most hip hop influenced anime I can think of, with Shing02 (born in 1975) being the Japanese rapper I’m most familiar with.

Street Fighter 3 3rd Strike (1999) had a hip hop influenced style.

Whether or not rap is “more popular” now can probably be answered by doing some research. www.billboard.com/charts/japan-hot-100/