Any thread can be a hazard,but that doesn't mean it will be. I used monofilament on quilts to send to college with my older kids 17-18 years ago. They are fine. Their kids use them now, no problems.
On the other hand, one DD as a baby nearly lost the end of a toe due to a thread in her sleeper. It wasn't a new sleeper, it had already been worn by 3 other kids. So while it can happen it probably won't. Mom's long hair can create the same risk.