If both parents are ginger, their offspring would be ginger. Reason: We inherit half our chromosomes from our father (23) and half from our mother (23), 46 in total. If both parents passed on a ginger ‘infected’ hair colour chromosome, the child would be ginger.
If one parent passed on a non-ginger chromosome, and the other a ginger chromosome, the child would be non-ginger, since everything other than ginger is dominant over the ginger.
Ginger is a recessive trait. With no dominant trait present in either parent, they can only pass on the recessive ginger trait to their offspring.
How non-gingers often end up producing gingers: For example – two black-haired parents give birth to a ginger child. How? Both parents have to be carriers of a ginger ‘infected’ chromosome. They have one ginger and one black each. The black would dominate the ginger, making them have black hair.
Neither would realize this, as all they would know is that their hair is black. They could both pass on the black, which would produce a black-haired child, one could pass black and one ginger, also a black-haired child, but if both passed on their ginger, the child would be ginger.
If one parent is ginger, but the other has no ginger gene, then their offspring would never be ginger, although all would carry the gene.