In dash and bash, an empty directory name in CDPATH means the current working directory so setting CDPATH to :/ has the same meaning as setting it to .:/. Fish doesn't have this default though:

dash$ export CDPATH=":/"
dash$ cd Desktop      #this works
dash$ cd ..
dash$ fish # Now lets see what happens in fish
fish$ cd Desktop
cd: The directory “Desktop” does not exist

The motivation for me reporting this is that this problem is a bit similar to the problem in #2090. Other shells might append to the CDPATH using CDPATH=$CDPATH:/blah and that will leave a colon at the start if CDPATH is previously unset. In that case, when Fish breaks it down into an array the first element will be the empty string.