I'm not an english speaker but that sentence sounds like wrong to me, I don't know why I think is because "for society" isn't well placed there.
The problem is not the position of "for society" but the absence of a grammatical subject. What is the subject of "isn't"?
We need a dummy "it" to function as an anticipatory subject of the real subject that is extraposed: "for a person to remarry."
The correct sentence would then be:
- For society, it isn't normal for a person to remarry.