What does it mean to "Use rendered output to group rows?"
Say you have a node with a taxonomy term, then a normal list would look like this


Title: A, Term 1
Title: B, Term 2
Title: C, Term 1
Title: D, Term 3
Title: E, Term 2
Title: F, Term 1
Title: G, Term 3


If you group them on the term, you would instead get something like this


Term 1


Title A
Title C
Title F

Term 2


Title B
Title E

Term 3


Title D
Title G



Rendered is not related to raw/safe values. It's just a way of explaining that it's the rendered (displayed) values that are used as grouping field.