I use cotton protectors with a plastic backing for both my kids right form the start and both are still alive. I have never heard of it being a safety issue. As long as you sleep baby on their back and give them lots of tummy time during the day to strength their neck they should be OK. I was far more concerned about getting a good change table that my baby couldnt roll off. The only injuries I have heard about from friends are there babies falling off change tables.