The bug
Nether portal blocks use one model for east-west portals, and another for north-south. The particle texture defined in models is used for determining both the texture used for particles and the texture used to display on top of the screen when inside of a portal. However, while having two different particle textures defined for the two different axes a portal can be oriented across works for the particle textures, it does not work for the screen overlay textures.
How to reproduce
Download and apply the attached resource pack
Build two nether portals, one on each axis
Punch (MC-167886) or destroy (then rebuild) both nether portals, noting the particles used
Enter both nether portals in Survival and note the texture displayed on screen
Expected results
The texture used for the particles would be different on each axis, as would the texture overlaid on screen when inside.
Actual results
The texture used for the particles is different on each axis as expected. However, the texture overlaid on screen is the same regardless of the direction of the portal.
This is a feature request.