Once Apple ID is signed in iPhone / Mac and iCloud is set up and keychain box is turned as on , over both iPhone and Mac , you should not disturb the iCloud Keychain settings as it will corrupt iCloud Keychain and various popups for iCloud Keychain will start appearing .
If you don't want to use keychain sign out both devices https://support.apple.com/en-in/HT208242
But you won't utilise iCloud features , once iCloud Keychain is set up there is no way to completely remove settings , the short cut way is sign out .
If you ever think that icloud keychain should never be set up in Mac erase the Mac hard drive and reinstall Mac OS , and never sign in with Apple ID and password and set up iCloud keychain .
Note : using third party apps to store passwords is avoided , setting up iCloud Keychain is more secured than any other apps ( but that is your personal decision ) .