seems Cloudflare has taken some steps to mitigate it, but I want to be sure if I need to disable GZip compression (something I really don't want) or do anything else to protect this site.
Do you mean is Plone, cloudflare, nginx or what? The reason I ask is because security is more than just at the web application layer...
The BREACH attack is exploited based on a combination of factors so it all depends on your deployment. The major weakpoint here is http compression algorithms.
Theoretically, Plone should not be vulnerable because we use a keyring of 5 randomized keys when issue tokens with secrets.
That being said, I've never done or heard of anyone that tested Plone against a BREACH style attack. For a Plone attack, the attacker would need to have an account on the target Plone site so that Plone will distribute the CSRF keys to the user. Then, I'm not sure how they get around the random keys used that plone employs.
I'm not sure if any of the things cloudflare has listed there actually fight against BREACH even though they claim it does. Everything they talk about is related to SSL compression.
In any case, if you're very nervous about the attack, you can disable compression just on text/html responses.
The effects of the HSTS Policy, as applied by a conformant HTTP user agent (UA) in interactions with a web resource host wielding such policy (known as an HSTS Host), are summarized as follows:
UAs transform insecure URI references to an HSTS Host into secure URI references before dereferencing them.
The UA terminates any secure transport connection attempts upon any and all secure transport errors or warnings.
The most CPU-intensive operation is the SSL handshake. There are two ways to minimize the number of these operations per client: the first is by enabling keepalive connections to send several requests via one connection and the second is to reuse SSL session parameters to avoid SSL handshakes for parallel and subsequent connections.
but, at least for me, it had no effect at all: nginx is using only around 1% CPU and that was mostly unchanged after that.