Muzan is indeed afraid of Yoriichi's breathing technique, sun breathing. But did not kill Tanjiro's family for that reason. Due to Tanjiro's family being descendants of a close friend of Yoriichi who was taught Sun breathing techniques, Muzan targeted the only remnant of Yoriichi, Tanjiro's family. In the manga, (SPOILER): All the remaining demon slayers fight against Muzan and before the Sun rises, Muzan takes over Tanjiro who if he remained as a demon, would be immune to sunlight and the nichirin blade. But through the support of his friends, Tanjiro managed to mentally defeat Muzan, defeating him as a result. Everyone is eventually reincarnated.
