Cats 😻😼and babies

Ok guys I thought I had a pic of my cat doing this but I don’t. So my mom is freaking out saying I gotta get rid of my cats cuz there going to try and suffocate my baby.( not intentionally.) but when I mentioned it to a few friends and my sister-in-law they all claimed it’s a myth like obviously I am not going to assume it’s safe and trust the cats. But I was hoping any of you who had kept your cats around after having your baby could give me some tips and advice on how to best keep both. (I wanna try and keep my cats but if it’s to dangerous I must keep my newborn safe over keeping g my pets.) my favorite of the two cats has been climbing inside the swing I got my baby and sleeping in there like it’s her bed now granted I spray her when I catch her so she knows it’s not allowed and she used to do it with the car seat till I hit the base inside so I am kinda hoping as long as there’s something inside she will not try and get in the good news is she stays. Away from the crib she used to sleep ontop of the changing table but now she just has lost interest completely so I am just wondering really what your cat and babies life’s have been like since I know family’s who have still kept there pets after the baby was born. Just want tips on how to keep baby safely and cats.