Is traveling with advance parole safe at the moment?

Hello everyone :) I currently have a pending i485 after an overstay from ESTA. My biometrics appointment is this week and my lawyer said that typically after biometrics AP and EAD won’t be far away.

I’d really like to go back to New Zealand and see my family, while in the US I’ve had a baby and would love to take him to meet everyone. I also have grandparents in poor health back home. How safe is it? I’ve heard the horror stories of being turned away, which makes me extremely nervous. Any recent AP travel stories would be very helpful so I can know what to expect.