If you agree to the terms, then you should sign the agreement. That simple. The real heart of the matter is your reference to your religious convictions. I doubt they have anything to do with signing agreements. I suspect your real issue is you disagree with divorce and I can appreciate that. I believe it is in Mark, somewhere around chapter 6 or 7, that Christ talks about how divorce was a creation of man because of our weakness. A divorce was allowed for adultery; however in the eyes of God if either party should re-marry that would still be adultery. This is true no matter how you cut it. Two people become one and no matter what attorney tells you other wise you will never be the same. I have had fellow Christians ask how in the world can I do divorce law and reconcile that with the Bible. Bottom line is, no reconciliation is needed. When you have someone, (your husband) break his vows, (adultery) there should be a means to where you can be free of your role as a Wife. This is a divorce, plain and simply. This agreement in question is proof that you two can be adults and work the property and support issues out.
Back to the religious issues.... Inevitably, you will find someone new and this in God's eyes is still adultery. God is trying to teach us as hard headed as we are, that when a marriage breaks down, both parties are at fault. We should make all efforts to preserve the marriage, but you can't always because we are sinful humans. Just like when you break your vows and sleep with someone else.
You can be divorced. But you both need forgiveness in order to have your own new separate lives. This is where God comes in, as always, to forgive, to love, and be our Father.