There are many businesses of questionable reputation in Kabukicho. These businesses attract somewhat dangerous people. There's little question that Kabukicho is the most dangerous neighborhood in Japan.
That being said — Tokyo is remarkably safe. Locals have little fear of Kabukicho. There are plenty of regular businesses in the area: restaurants, karaoke, arcades, etc. Tokyo people go to these places without a second thought for their safety.
A few tips for staying safe in Kabukicho:
1. Don't visit bars unless you're sure they're safe. It's not a good neighborhood for random bar hopping. If it looks dangerous — it probably is.
2. Stay sober. Kabukicho isn't a safe place to be intoxicated. Most people who have a bad experience in Kabukicho are intoxicated when it happens.
3. Be careful taking photos of people in Kabukicho (some people won't like it). A red light district filled with people doing things they aren't proud of — isn't a great place to start taking photos of strangers. Yakuza don't particularly like having their photo taken either. Even police in the area are known to be aggressive against adventurous photographers.
4. Never go anywhere with a tout. There have been scams reported where foreigners are lured to a bar by touts. They are then presented with an outrageous bill and tough bouncers demanding immediate payment. In other variations of the scam, customer's drinks are spiked and their wallet stolen.