It's one thing for them to decide which of their friends and family they tell about what's going on in their lives. But frankly, they have no right to control which of your
friends and family you
tell about what's going on in your life
I know people who have left otherwise happy relationships over not wanting to be a dirty little secret, and I can relate. I would never date someone who tried to keep me in the closet.
It's not that I can't understand their position. More that this is one of those things that is best to discuss before you really get involved to the point that there's "something to tell." When you get romantically involved with someone, the natural tendency is to sing your happiness to the world. If someone intends you to do otherwise, they ought to tell you at the beginning.
So then the question is, what do you do about it going forwards? Given that you now know they're planning to keep you a secret from everyone they know, including mutual acquaintances, are you willing to continue the relationship on that basis?
Also, please visit and direct them to this link
. It will bring up some other points that you all need to discuss -- better to get it out in the open now rather than wait.