As an SO myself, I always leave that decision (whom to come out to) to my boyfriend! Nobody else has the right to make that call.
Like most people have said here, I would ask: What is the exact *reason* your SO wants to hide your history? And how does your SO's reasoning make you feel?
In our example, we've informed (or not informed) my family members on a case-by-case basis. An aunt who is very progressive and has had trans friends, was told right off the bat. It felt good to have someone inside my family understand. Next, my mom was told but only after she'd gotten to know him a couple of times, so that she could think of him as a full complex person instead of as a caricature (that she might make up in her head) with TRANS stamped on his forehead.
Currently, no one else knows. We might tell others, might not. I have a sibling who is not a bigot himself, but lives in extremely bigoted ranch country (I know, I grew up there!), and I don't trust him not to "talk." All it takes is one extreme person, to compromise my partner's safety. Maybe I am being paranoid, but, yes I do fear for his safety a bit in that situation, so I told him I was against telling that sibling, for now. In a safety situation, not only the trans partner but also the SO could be endangered. So where serious bigotry from the SO's family is involved, I say the question of how much to be "out" should be a joint decision.
Elizabeth A.