Is it bad for a parent to kiss a 2 month old baby on the lips?

No. A parent has the right to kiss a baby right on the lips. The baby is a parents child and a parent has rights over the baby. That is my opinion.

Of course parents can kiss their babies on the lips, however if the parents have had cold sores in the past, ( a herpes virus) then they take the chance of passing on the herpes virus to their baby.