You can still safely compress your static files. So, assuming that you don't send any secrets in your CSS, JS etc., you can configure your server to enable gzip only for these resources.
For example, when using nginx and with gzip off globally, you can do :
Doesn't matter if they share cookies. Static files reflect neither user-supplied data nor secrets in their contents, so they can't be used in a BREACH attack.
For example, when using nginx and with gzip off globally, you can do :