Entering a Nether portal whose paired portal is oriented along the other axis (North-South to East-West, or vice versa), will cause the player to rotate 90 degrees clockwise during teleportation. For example, if I enter a W-E oriented Nether portal facing East, I will come out facing South. 

What I expected to happen was...:
I expected to come out of the Nether portal oriented in the same direction as I entered. 

What actually happened was...:
I entered the W-E oriented portal facing East, and came out in the Nether facing South. 

I left the Nether facing South and came out in the Overworld facing West.

90 degree rotation occurs no matter which orientation I enter the portal. 

Steps to Reproduce:
1. Make/enter a Nether portal
2. If necessary, break and re-orient one of the portals so that it is oriented perpendicularly to its counterpart
3. Enter the portal

Notes: I first noticed this in a Realm that has been updated from 1.15.2 -> 1.16.1 -> 1.16.2 after the 1.16.2 update, but was able to reproduce this in a 1.16.2 singleplayer world. This did not occur in previous versions in the Realm; I remember being conscious of facing the correct direction relative to the exit portal and there was no automatic rotation involved.