This issue, while a lot more emotionally regarded than others comes down to basic preparedness. Do we have the paperwork in place to prove, or assign our legal rights and wished regarding our health. We can't assume any more that hospital staff will take care of this for us.
There will be that staff member with an attitude that will use their beliefs to influence their actions. But the world is changing. Family can be all kinds of different things. I have a friend who's family consists of herself, her daughter and two female friends who share her home with their daughters. No they aren't gay.. but they are a family.
Another friend lives with her father and her father's maiden aunt. Again.. family, sharing a home, sharing expenses, caring for each other. My boys live in large communal type living arrangements. They share a home, celebrate the holidays together, and are very much a family.
So, if you want your rights to be acknowledged.. do the paperwork. If you want your partner to inherit.. make a will. If the paperwork is done you can leave it to your spouse, your caregiver, your sexual partner, your next door neighbor or your pet cat.
Today's world has become so complicated that there no longer can be the assumption that the local healthcare facilty will just 'know' that its okay to let you in. I face this as a mother of adult children. I went in to the doctor's office with my son after he broke his leg with my checkbook and they wouldn't let me pay his bill until he signed paperwork authorizing it and he was standing right next to me at the time.