From the 1.16.0.51 beta changelog:

• Piglins that somehow end up in the overworld become zombified fairly quickly

Note that the changelog only mentions piglins becoming zombified piglins in the overworld.

However piglins are able to become zombified piglins in The End. Could be intentional due to MC-172107 being reopened.

Observed Results

Piglins shakes and transforms into zombified piglins in The End.

Expected Results

Piglins stays as piglins in The End. (MC-172107)