how to allow ECS task access to RDS
IAM roles and Security Groups are two totally different things that serve different purposes. You have to open the Security Group to allow any network traffic to access the RDS server. Instead of whitelisting the IP address you should whitelist the inbound Security Group.
For example if the RDS server is in Security Group 1, and the ECS server is in Security Group 2, you can enter the ID of Security Group 2 in the inbound access rule of Security Group 1. Then you don't have to worry about servers changing IP addresses.