Currently I sign into my Stack Exchange account using my Google login. I'd like to replace this with a different login method, though, so I can still log in to Stack Exchange, but not with Google.
How can I do this?
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Click "add more logins" and pick a different sign-in method. There are some more detailed instructions (with screenshots) here.
Once that is set up, you will be able to remove your Google credentials from the same dialog: go to "my logins" from your profile and click "remove" beside the credentials you want to take out.