Continuous Delivery is an extension of Continuous Integration. CI is all about evaluating your changes in the context of everyone else's on a frequent basis (if you commit less than once per day it can't count as CI)
Branching, of any kind, is all about isolating change and so is fundamentally at odds with CI. Feature branching and CI are opposed.
What most organisations do is merge branches before testing. This compromises the value of the feature branch, but retains the value of CI. If you don't do this then the CI has little real value for the reasons that you describe - you are not evaluating changes in a realistic context.
Sorry but you can't have both, they are opposites!