If they do, they arent worth your time. That goes for people who go public thinking things about those who go private.
Its a very individual choice.

I went public with my son and again this time, different hospitals though.

Both times I saw the same carer throughout my pregnancy, and this time its acaseload/one midwife program so she or her backup will be on call when I go in to labour/for birth.

If I wasnt low risk and needed to see an OB then I would probably consider going private, as the OB I was with my first bub is less available now, and I dont like his backup OB.

It all depends on your circumstances, but other peoples opinions of you shouldnt come in to it.