I do not see a problem here at all. The article states that these advice books are reviewed at least annually, so changing "Dad" or "Mum" to "partner" incurred no additional costs to the NHS. You could also say that those adopting a baby should not be called "Dad" / "Mum" as they are not the birth parents
It actually stikes me that this person is somewhat homophobic... from the article:
Norman Wells, of the Family Education Trust, said the NHS was wrong to change the language in the booklet."
He said: "The NHS should not be squandering tax payers' money to advance the cause of a minority interest group."