There are two dominant types of crosses, which reflect two Christian interpretations of the meaning of Jesus' death & resurrection. One cross, normally called a crucifix, has a figure of Jesus on it. The other cross has no figure of Jesus on it.
With some exceptions, most people who wear a crucifix endorse a scapegoat theology, that Jesus' sacrifice was demanded by God to recompense for the sins of all humanity. Many people who wear a cross accept a resurrection theology — that ultimate good will overcome the worst evil.
I consider myself among the second group. I do wear a cross, a James Avery Celtic-inspired design, with no figure of Jesus. I find the notion that God demands any sacrifice, whether human or "lower" animal, to be repugnant.
We humans demand sacrifice, because we tend to see things in extreme polarities - e.g., good and evil - which must be balanced. If we are wounded in any fashion, our first impulse is to seek revenge. When slapped on the cheek, most people must resist the urge to slap back.
Our notion of God has traditionally been in human terms. So it's not surprising that we think God has the same need for revenge that humans do. We suppose our sins wound God in some fashion, and that God will seek to restore balance by punishing us.
Forms of sacrifice have been common to many different religions across many different cultures throughout history. At the time of Jesus' execution, animal sacrifice was the accepted ritual. We have inherited that model, and continue using that language.
Although being "washed in the blood of the Lamb" seems unwholesome, icky, and altogether treyf, whether one is Jew or goy.
My opinion is that God does not demand any sort of sacrifice. If one has sinned, let that one make amends in his or her own fashion - to do justly, love mercy and walk humbly with God, to paraphrase the prophet Micah. In the Gospel according to Mark - the earliest of the written canon - there are only two statements Jesus makes about his death which might be interpreted to indicate that he perceived it to be a sacrifice to benefit humanity (see Mk 14:22-25). The bulk of this Gospel is devoted to how humans treat each other, with how we may enter into relationship with God.
