Installing GPU-enabled TensorFlow on Mac is a torture. It takes hours to find the right tweaks. While there are only few people using NVIDIA GPUs on their mac because of recent adoption of AMD chips, this instruction will still benefit the users of Hackintosh or old Mac Pros. I'm not sure whether this will work on eGPUs, if it does, it could be great news for other Mac users with their purchase of eGPU boxes like Razor Core or Akitio Node.

  My System:
   i5-4690k
   NVIDIA GeForce GTX 970
   macOS 10.12.3
   python 2.7.12
   TensorFlow 0.12
   Xcode 7.2.1/8.2.1
   cuda 8.0.54, cudnn 5.1, nvidia-367

1. Keep two versions of Xcode: Xcode7.3 (7.2 also works) and Xcode8.x

2. Set Xcode directory to Xcode8, update brew, cask, bazel, cuda as Official setup guide
   Change directory of Xcode to the right version (may be somewhere else):
   sudo xcode-select -s /Applications/XCode8.2/Xcode.app/
   You can type gcc --version to check LLVM version

3. Set Xcode directory to Xcode7 to compile cuda samples to test whether the installation is a success. Don't forget to add cuda path to ~/.bash_profile
   export CUDA_HOME=/usr/local/cuda
   export DYLD_LIBRARY_PATH="$DYLD_LIBRARY_PATH:$CUDA_HOME/lib"
   export PATH="$CUDA_HOME/bin:$PATH"

   After installing cuda type in
   sudo ln -s /usr/local/cuda/lib/libcuda.dylib /usr/local/cuda/lib/libcuda.1.dylib`
   to create symbolic link so as to prevent segmentation fault when importing TensorFlow later

4. Choose the right distribution of TensorFlow and pip install it. You can try, but most likely, python will fail importing TensorFlow

5. Then try installing TF from source.
   git clone https://github.com/tensorflow/tensorflow
   cd tensorflow
   Now you are in the TensorFlow workspace. Run ./configure to set directories and versions
   Choose default except for cuda to enable cuda
   Currently, enter cuda version as 8.0 and cudnn version as 5 (though 5.1 in fact)
   Check GPU computability on Nvidia's website:
   https://developer.nvidia.com/cuda-gpus
   According to the official installation guide, when done configuring you should enter
   bazel build -c opt --config=cuda //tensorflow/tools/pip_package:build_pip_package
   to start building. However, most likely it will throw you an error dyld: Library not loaded: @rpath/libcudart.8.0.dylib
   To solve the problem see https://github.com/JimmyKon/tensorflow_build_issue_fix/tree/master
   You will have to modify the genrule-setup.sh in your temp folder following the instructions.
   You can search or find it here:
   /private/var/tmp/.../execroot/tensorflow/external/bazel_tools/tools/genrule/genrule-setup.sh
   After modification, run ./configure in TensorFlow workspace again and start building with
   bazel build -c opt --config=cuda //tensorflow/tools/pip_package:build_pip_package
   This will take a long time, enjoy your life. Continue with
   bazel-bin/tensorflow/tools/pip_package/build_pip_package /tmp/tensorflow_pkg
   sudo pip install --upgrade --ignore-installed /tmp/tensorflow_pkg/tensorflow-*.whl
   If you are using something like anaconda, --ignore-installed is necessary, sudo is related to your pip install

At this time, try importing TensorFlow in your python. If it throws you a keyerror:...
Try installing this version of protobuf provided by Google
sudo pip install --upgrade https://storage.googleapis.com/tensorflow/mac/cpu/protobuf-3.1.0-cp27-none-macosx_10_11_x86_64.whl
I don't know whether there is a proper GPU version, this version is working on my system. If it doesn't work for you, try
sudo pip install --upgrade protobuf

6. If you encountered other errors, check the official setup guide for more information.

Reference
https://www.tensorflow.org/get_started/os_setup
https://srikanthpagadala.github.io/notes/2016/11/07/enable-gpu-support-for-tensorflow-on-macos
https://github.com/JimmyKon/tensorflow_build_issue_fix/tree/master