Wither Skeletons will not chase a player into sunlight/daylight, even though they do not burn during the day.
(This is an old bug that has went unfixed for a long time.)
How to recreate:
Spawn a Wither Skeleton in the Overworld, sheltered from sunlight.
Enter Survival Mode, and have the Wither Skeleton attempt to chase you, whilst stepping out into the sunlight.
From here you will be able to observe how the Wither Skeleton refuses to step out from the shade, and will not enter the sunlight, even though it would not be harmed from the sun.
We're tracking this issue at MCPE-44218, so I will resolve and link this report as a duplicate.
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