Hi, Is it safe to use a mattress protector that is made from cotton with polyurethane backing? If my baby rolls on to their front will they be able to breathe through this? Thank you.

Red Nose recommends that baby be placed on a mattress that is firm, clean, well-fitting & flat.
It is important that the mattress protector does not compromise the firmness of the mattress, not necessarily the fabric of the protector.

A safe mattress is one that is the right size for the cot, is firm, clean and in good condition and is placed flat (not tilted or elevated).
A soft mattress or sleeping surface can increase the risk of sudden unexpected infant death if baby rolls over onto the tummy.
.....always make sure that the waterproof mattress protector is strong and a tight fit.
Never put soft bedding under the bottom sheet, such as a sheepskin, as this makes the sleeping surface too soft.
https://rednose.org.au/article/what-is-a-safe-mattress

Remember, that most babies will be rolling by 4-6 mths & many will prefer to sleep on their tummy.
It is especially important that the baby is slept on a firm, flat mattress.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over