"Andi is reading out the new school rules."

Translation: Andi membacakan peraturan sekolah yang baru.

[JamesTWils]

Without "yang," would this mean "the rules of the new school"?

[Rick392366]

Without "yang," would this mean "the rules of the new school"?

Yes, that's correct.
'peraturan sekolah baru' ==> the rules of the new school.

'peraturan sekolah' ==> the rules of the school.

'yang' refers to the head noun (peraturan).

'peraturan sekolah yang baru' ==> the rules of the school, which are new.

[ChrisNeedh5]

Wouldn't "Andi membacakan peraturan-peraturan sekolah yang baru" also work, given that 'rules' is plural?

[hayatisega]

The sentence can mean rules about the new school, or new rules (of the same school)