It depends a lot on what the application is logging to begin with.
If a project prints passwords in logs, consider to just GTFO as it's terrible security practice.
There might also be sensitive info that's not coming from a static thing like your username, but from variable data such as IP addresses, gps coordinates, or whatever thing gets logged.
Meaning a simple find&replace might be insufficient.

When possible, I tend to replace the info I remove with a short name of what I replaced out as it's easier to understand context when it's not all ********** or truncated.
example:

proxy_container_1     | <redacted_client1_ip> - - [17/Aug/2024:12:39:06 +0000] "GET /u/<redacted_local_user2> HTTP/1.1" 200 963 "-" "Lemmy/0.19.4; +<redacted_remote_instance3_fqdn>"

keeping the same placeholders for subsequent substitutions helps because if everything is the same, then you don't know what's what anymore.
(this single line would be easy enough either way, but if you have a bunch and can't tell client1 from client50 apart anymore that can hinder troubleshooting.

regular expressions are useful in doing that, but something that works on a specific set of logs might miss sensitive info in another.

I'm sure people have made tools to help with that, possibly with regex patterns for common stuff, but even with that, you'd need to doublecheck the output to be 100% sure.

It helps a lot when whatever app doesn't log too much sensitive info to begin with, but that's usually out of your hands as a user.