My boyfriend is a convicted sex offender in the state of MN against an adult. Will he be able to parent our expectant twins?

You already expect twins? If so and he is the culprit then he has already fathered them. Whether he can parent them is a more complicated question which requires a consultation with a MN lawyer.

Can't accurately say without more information. Your best option is to consult with a local criminal attorney who would need to review the specific details. Best of luck.

There are no rules about who can parent children. Even murderers are allowed to have children. Assuming that he is no longer on parole or probation, there is nothing preventing him from being around children. The only reason he could not parent his children would be if he is subject to some supervision that prevents it. If he is on supervision relating to this or some other conviction, he needs to check the conditions to be sure there is no condition preventing him from being around children. Given that has never committed a crime against children, that seems unlikely.