What I mean is, I'm constantly copying passwords to my clipboard, both to generate them and to input them. This is an app which remembers clipboard history. That means all my passwords will be stored in this history, which makes it incompatible for my use case.

The documentation is less than clear about whether it can ignore apps:

By default, Alfred ignores popular password applications like the macOS Keychain Access and 1Password, so that you don't inadvertently copy a password to your clipboard.

I don't want to prevent apps from copying to my clipboard. I want to prevent Alfred from storing the history when I copy from a specific app (my password manager).

I may as well just try it and find out, though.