Thank you for all of the nice comments. What if the reason is because the other’s parents would never be willing to accept it?
So I have experience with this. My D started dating a young woman at college earlier this year. It wasn’t a shock to me, I have known for some time that she liked women, but she did also date a boy for a while. So… it is good that I am a pretty flexible person. 
I was coming to campus for Thanksgiving break, as I usually do, and I take D and whatever friends she wants to invite out to dinner. I suggested to D that she bring her new GF, as I would love to meet her (she brought the boyfriend a couple years ago, so this is not unprecedented).
D said her GF wasn’t comfortable – she comes from a family that would NOT be accepting of her choice, and couldn’t quite get her head around the fact that I was fine with their relationship. So the GF did not come along, and I didn’t meet her. D ended up breaking up with her a couple months later.
OP, regardless of how the GF’s parents feel, I would want to meet the GF. And I wouldn’t spill the beans at graduation or something if the GF wasn’t out to her parents.
I’m with @intparent on this—and also, remember that there are plenty of reasons that a parent of one or the other in a relationship mightn’t like someone, whether it’s gender or religion or race or social class or simply the fact that somebody had a bad experience once with someone who has red hair. If you were in a relationship with someone whose parents wouldn’t approve of you because of your race, would you hide the relationship from your own (more accepting) parents? In fact, that might be a situation where both of you might need the support of your parents more than ever.
OP, first, thank you for not flaming me when I posted what I did. I have a close relationship with both my sons (sometimes they tell me too much!) so if they didn’t share a long-standing relationship status with me, it would be 1) shocking, and 2) hurtful. I really was just answering honestly for me and my situation.
To answer this last question, I guess it would somewhat depend on the logistics of it all. If your gf’s parents are far away and wouldn’t be accepting of the relationship, I can see why your gf might want to play it all close to the vest. There’s a lot I didn’t tell my parents, but they generally weren’t accepting of almost any of my choices.
So, I’m assuming the gf isn’t out? Regardless, I don’t see why the fact that her parents wouldn’t accept the relationship would affect what you tell your parents. Or are you now asking for her?
Even though you are my daughter and I am your mother, as adults we are best friends. And you tell your best friends everything. Please do not leave me out of your life.
If your parent is accepting but your partner’s parent(s) are not - that may be even more reason to have an open relationship with your parent - you and your partner will likely benefit from the support - even if it is just from one side.
I’d want her to know that her life will be so much easier, and will bloom, when she feels confident enough to be herself 24 hours a day. I would tell her to please invite her partner to meet us!
OP may think most parents posting on this thread are more of open minded, and maybe not representative of general parents out there.
I just want to add an anecdote. I have a friend who is extremely conservative and very macho. HIs view of women and guns often made me cringe. Recently we were talking about our kids. He told me that his younger daughter was confused about her sexuality. He thought she may be gay, but she was not sure yet. I asked him how he would feel if she was gay. I expected him to say how disappointed he would be (or something to that sort), but instead he said, “I love her no matter what. I just want her to be happy.” I asked him if she knew because I was surprised by his reaction.
I think most kids would be surprised how accepting parents could be because of our love for them.
But not all—and there’s the risk.
Good communication is golden.
So OP do the parents already know each other? If so I can see where it maybe hard to tell one set and worry about the other set finding out.