As someone who works in Python almost every day, I have a lot of environments on my machine, and I wanted Blender to use a version of Python other than what it was inexplicably intent on using after renaming the “python” folder.
Thankfully, I found a solution. This should work easily for Mac / *nix users, but Windows users often don’t realize that you can create a symbolic link in the file system. This means creating a link in Blender\2.78\ called “python” that acts like a folder, but actually silently redirects to somewhere else.
On Windows, this can be accomplished with the mklink command and the /J option, such as below:
mklink /J “C:\Program Files\Blender Foundation\Blender\2.78\python” C:\Anaconda3
ADDENDUM:
To be clear, you should still follow Ben’s advice of renaming both the default python folder AND dlls first.