It would really depend on your baby. My cousin never changed her detergent and her daughter was fine. My son has extremely sensitive skin so we had to buy the white bottle.
I switched to eco sheets a year ago for mine and my husband’s clothes, when I was prepping my baby’s clothes, I checked the label and it is also safe for babies. Maybe switch to something non toxic with less allergens for all of you so you don’t have to think about it when washing your baby’s clothes.
I've always used non-bio for myself so use it for baby too. But I learnt recently that most countries don't sell non-bio, only bio and it's actually the scent that irritates skin.
Its probably fine, but you have plenty of time to re-wash it if you're worried! You can just put it in again with no detergent and run a rince cycle if your machine has one.