My sister-in-law's baby's dad is a sex offender. She's wondering if the dad can get shared custody with her.

Depends on the conditions of his conviction and his level/status.

With what little info you gave us yes. What she will need to do is prove he is a threat to his child.

A sex offender can be someone who urinated in public,
A sex offender can be someone who was 19 and had sex with a 15 year old,
A sex offender could have hired a hooker who turned out to be 17
So why are they a sex offender, is those actions related to the child and a threat to the child.

As the father of the child, did the mother leave the child alone with him to help care for child ? If so that proves the mother has no free of the father to the child.

So tell us the story highlights.