In a 'kokushibo meets tanjiro fanfiction', one possibility is that Kokushibo senses something different about Tanjiro right away. Maybe it's the fact that Tanjiro has a unique scent or an energy that Kokushibo has never encountered before. Tanjiro, being Tanjiro, would be ready to face Kokushibo head - on, but also be open to communication if there's a chance. The story could explore their different views on the world of demons and slayers, and how they might come to understand each other better through their encounter.
For Tanjiro, he could become more understanding of the complex nature of demons. Meeting Kokushibo, a powerful and complex demon, might make him realize that not all demons are simply evil. Kokushibo, on the other hand, could start to have some doubts about his loyalty to Muzan. Tanjiro's tenacity and belief in the good of all might start to chip away at Kokushibo's cold - hearted exterior.
Maki in fanfiction usually has a fierce loyalty to her friends, especially Yuta. She is the type to fight for what she believes in. Yuta is sometimes portrayed as being a bit naive in the ways of the world outside his own small circle, but his pure heart makes him endearing. In many stories, their different personalities create an interesting dynamic, like in a story where Maki's boldness gets them into a risky situation and Yuta's calm thinking gets them out.
The battle of Yoriichi vs Kokushibo can be found in the advanced stages of the Demon Slayer manga. It's an intense and highly anticipated confrontation. The build-up and action are both masterfully depicted.