Tensorflow with CUDA 9.1 and cudnn 7.05

There seem to be some problems with cuda 9.1 and tensorflow, and it seems that the tf team doesn’t plan to build against 9.x at all. (https://github.com/tensorflow/tensorflow/blob/master/RELEASE.md) Is there a recommended way/tutorial to build tensorflow with cuda 9.1? Or is the official recommendation to go back to CUDA 8?

The page you linked to seems to spell out all necessary details. I don’t see what is unclear about it:

If you use the XLA feature you will either have to wait for a fix in a future version of CUDA or go back to CUDA 8.

For all other uses, CUDA 9.0 seems to be the officially blessed version.

I have been round this loop on Mac OS X. Here is how I eventually resolved it.
First. I had upgraded to High Sierra 10.13.3 build 17D102. This generated a persistent “CUDA needs upgrade” warning on start-up even though the screen showed that my version (387.128) was the most up-to-date (March 2018).
The problem was (in part) that the GPU driver greyed out underneath was clearly very out of date.
Second. All attempts to download a CUDA driver met with a Mac OS X incompatibility warning before a CUDA9.1 was issued compatible with a 17D102 build which I read about at https://www.tonymacx86.com/threads/nvidia-releases-alternate-graphics-drivers-for-macos-high-sierra-10-13-3-387-10-10-10-25.243857/ . If you are looking for a different recent build, that page may have your build link on it.
You can find that build at https://images.nvidia.com/mac/pkg/387/WebDriver-387.10.10.10.25.161.pkg
Third. Tensorflow-gpu in all the available versions for pip3 install (since tensorflow stopped supporting Mac OS X as of version 1.2) looks for CUDA8.0 and throws up a runtime error on import tensorflow as tf because it can only find the 9.1 library.
Fourth. Damian Broncel has built a wheel with CUDA9.1 and Tensorflow_1.16.0-rc0. The instructions both on a source install and on the whole process including e-GPU using the wheel are here: https://byai.io/howto-tensorflow-1-6-on-mac-with-gpu-acceleration/ but you seem to have to install CuDNN1.0.5 even if you use the .whl package.
Fifth. Everything now works including the GPU tensorflow validation scripts and as a bonus the fascinating NVIDIA CUDA samples.

Is the tensorflow issue with CUDA Toolkit 9.1 only affecting the XLA feature of TensorFlow (which is described as ‘experimental’, so we won’t use it for now) or does it affect core ports of TensorFlow ?
(Visual Studio 2017 Release 15.4, TensorFlow 1.8, Cuda Toolkit 9.1, CUDNN 7.1)