What functions are disabled with noInterrupts()?
From what I found turning off interrupts will definitely disable incrementing values of micros() and millis() This means that also every method that uses them like delay() will also not work correctly.

Of course manually attached interrupts using attachInterrupt() will also not work as intended.

According to comments by @Juraj Things that also will not work are Serial interrupts. Also libraries like Wire require interrupts for their logic.

EDIT: @EdgarBonet You are right, I removed incorrect info.