The problem is caused by ButBucket identifying a user by first SSH key he or she supplies. There are several workarounds for this problem, but the one I prefer is to use ssh Host alias. In your ~/.ssh/config file add section like this:
Host bitbucket-cm
HostName git.bitbucket.com
User git
IdentityFile ~/.ssh/id_rsa.1
IdentitiesOnly yes
This would basically create a SSH host alias bitbucket-cm for git.bitbucket.org associated with id_rsa.1 key. Now, instead of usual checkout URL, say,
git clone git@bitbucket.org:org/repo.git
use:
git clone git@bitbucket-cm:org/repo.git