In recent years, there is a noteworthy advancement in autonomous drone racing. However, the primary focus is on attaining execution times, while scant attention is given to the challenges of dynamic environments. The high-speed nature of racing scenarios, coupled with the potential for unforeseeable environmental alterations, present stringent requirements for online replanning and its timeliness. For racing in dynamic environments, we propose an online replanning framework with an efficient polynomial trajectory representation. We trade off between aggressive speed and flexible obstacle avoidance based on an optimization approach. Additionally, to ensure safety and precision when crossing intermediate racing waypoints, we formulate the demand as hard constraints during planning. For dynamic obstacles, parallel multi-topology trajectory planning is designed based on engineering considerations to prevent racing time loss due to local optimums. The framework is integrated into a quadrotor system and successfully demonstrated at the DJI Robomaster Intelligent UAV Championship, where it successfully complete the racing track and placed first, finishing in less than half the time of the second-place.