We have a website hosting with AWS Elastic Beanstalk and are using the eb deploy command to upload changes, etc... The issue I am having is it seems to overwrite any files that were uploaded using the WordPress dashboard when I deploy new changes. I tried adding wp-content/uploads to my .ebignore but then all images on the website are dead. Is there a way to not overwrite this folder at all?
You should never upload files to a server running on Elastic Beanstalk. Those files will be lost at some point, either during a deployment or a scale-in event or something else. The only method of making changes to your EB server should be through the eb deploy command. In addition that method of storing files will not work at all once you scale up your EB environment to multiple servers.
You should be utilizing the AWS S3 service for image storage. There are several Wordpress plugins that facilitate storage of images on S3.