I would like to suggest the possibility to add attributes for a branch, and send these attributes in the webhooks.
Such attributes would be configuration which is not of interest to check in, and only apply for a specific branch.
DebugLevel = x
TestA = enabled
These attributes would be sent in each webhook, and can be used by the ci machine to build/test/deploy the branch in a special way.
It is of course also possible to keep this information close to ci, but it is preferred to have possibility to add/remove/view attributes via the bitbucket gui.