Ok I think you need to have a very hard think about what kind of life you are actually looking forward to here.
Firstly, as others have said, he will not have received a sentence, and presuambly be on a lifelong register, for anything that could be excused as minor. He will have raped or seriously assaulted a child. Think about that.
Then think about this. The person you describe as 'good grandmother' material will know the details of this crime - what he did to a child. As a mother herself, she knew this, and was still attracted to, would climb into bed with, would marry this man and let him take a parental role with her own child. There is so much wrong about that I'm not sure where to begin. To say her judgement is skewed would be the kindest way of putting it. More realistic would be to say that I wouldn't let a woman like that near to or in any position to influence my child as they simply wouldn't be safe. Someone who can excuse violent sexual crime and paedophilia to that extent is disturbing in themselves. Someone who can be sexually attracted to someone like that disturbs me. Things were presumably different then re checks otherwise she would have had your BF removed by social services for her actions in having a relationship/marrying this man. Think about that too.
And then there is your partner. You should be most worried of all that the man you see as the future father of your children has been brought up with such a skewed notion of what is ok that he hasn't told you about his stepdad - worse, that he sees this man as so much not a problem that he still IS his stepdad, a trusted relation. This isn't something you can negotiate on and it should panic you. When you have children, you might quite happily decide there's no contact with MIL and her H but there seems every chance your H will disagree. Or worse, as he has shown he's capable of, just not tell you that he's taking your child to see them. There's not a lot you can do to stop that. You can't constantly protect your child when the father will very likely undermine that because he doesn't see anything wrong in his stepdad being a convicted child sex offender. At least, not without divorce and a lengthy court case over access. There's every chance your partner may have been abused too.
Don't take your MIL's telling you as proof of any finer feelings. She may be looking for a way to leave her H. More likely, it may be that someone has worked out the situation now that you've moved in together and has threatened to tell you themselves.
The first thing I would do is approach the police and explain the situation and ask if you can apply for a disclosure. I would hope that what you read would be enough for you to rethink having children with this man at all or being part of this fucked up situation. My feelings are that your views on this would change very suddenly and dramatically when you do have a baby. By which time it would be too late.