It means something particular. This hospital visitation business is small hurdle to get over. That's not the real issue. Rather, this is an attempt to change a long-standing institution for the purpose of getting public acceptance of a lifestyle that most people think is undesirable and immoral. This is where the question of family values comes in.
Family values is a specific thing.
It means something particular. That's why we call them traditional. Something is amiss here. Traditional values aren't new, and if they are new, they're not traditional. It refers to something that has a longstanding history of being accepted by the mainstream of society.