Can I change the needle size for the Paralleogram scarf from 3.75mm to 4.5mm?
You can use any needle size that you like but it will change the amount of yarn you use. That said, in the case of this scarf it won’t really matter I don’t think.
The suggested needles are always a guideline. If you swatch with a 4.5mm and like the fabric that you create, then yes. If the gauge is affected by the change your dimensions will be different and you may need a different amount of yarn.
I have knit two of these Parallelogram scarves, one using the prescribed yarn, needles and Cast on stitches, the second with slightly heavier yarn and more stitches. I’d strongly suggest making a sizable swatch before you start. It takes a while for the stitches to develop into the pattern you see photographed. Judge by the fabric you produce. If it looks too loose to you, you probably won’t like it in the long run. Very slippery needles are not great; try bamboo or carbons.