Windows – Unable to push to remote Git repository, reading response from git-gui–askpass failed

Both answers I got mention permissions but that I had already checked. Both ~/.ssh/id_rsa and ~/.ssh/id_rsa are owned by my user with 664 and 600 respectively. I even tried chmod 777 to both files but got the same message.

777 permissions will never work. SSH permissions are highly restrictive and opening them up more like that will only cause errors. Also your comments to other questions state that these are your current permissions:

-rw-rw-r--. 1 centos centos 47 May 17 20:33 /home/centos/.ssh/config 

Those are 664 permissions which are -rw-rw-r--. What you want is 600 permissions which would be -rw-------. So please try this; first change the ~/.ssh/config permissions like this:

chmod 600 /home/centos/.ssh/config

Now do the same for ~/.ssh/id_rsa

chmod 600 /home/centos/.ssh/id_rsa

Also, I am not too sure what the Bitbucket SSH domain/user combo would be but it might be worth it to debug the process by using the SSH command with the -v (verbose) flag to see in detail what is happening. A command like this would help:

ssh -v -T git@bitbucket.org

The -v would be the verbose output and the -T would be setting SSH to “disable pseudo-tty allocation” so it would not be creating a real interactive session; it will essentially just attempt to connect to the remote host and then drop the connection. Useful for testing.

Behind a firewall, ...github ... Chrome uses our certificate for this access.

Based on this description I assume that "our" certificate is not the original certificate for Github but that you are using a firewall with SSL inspection which generates its own ("our") certificate to a man in the middle the connection. The CA in the firewall which issued this certificate (proxy CA) is probably added to the Windows Trust Store and this Chrome will trust it.

But Git doesn't use the Windows Trust Store and thus doesn't know about this proxy CA. Therefore you need to add the proxy CA used by the firewall to the CA store for the Git and not the original CA which issued the certificate for Github.