You should quit. I know you have reasons, but continuing to work at a place like this is not ethical.
I'm guessing you're referring to someone's ability to actually fix it -- in the case of logs, you can make a pretty simple regex to strip out all kinds of PII, and there really are a lot of arguments (e.g. proactively reducing cost of security audits -- if someone is reviewing your logs to figure out what happened, they might not want to see customer data).
(switching sides of argument, I know)