The bug

When moving through a nether portal, the overlay appears and progressively becomes more opaque. In the loading screen, it is entirely opaque. However, the transition from the overlay fading in to the loading screen is a sharp, instant change from translucent to opaque, as it doesn't reach full opacity just before going through the portal.

How to fix

Make the portal overlay go fully opaque just before the player is teleported through the same gradual fade.

Further notes

I'd strongly recommend making the teleportation overlay its own texture (a copy of the existing nether portal overlay but without the alpha channel), somewhere in the gui folder, as to prevent any resource pack conflicts/breakings this fix may cause.