Most of us don't have to worry about having touched something dead, but the foundation of these rules is the notion of being mindful of our actions and of the need to live a life set apart and different. While Christ came and provided the perfect and eternal sacrifice for our sins, we are called to "be holy, for I am holy." As followers of God, we are to seek His will.
While we often worship in more casual settings, dressed more casually, sometimes that leads us to forget that we are not going to coffee with our BFF. We are coming to worship the Creator of the Universe, Almighty God, and a certain degree of reverence and respect is warranted. Reverence and respect doesn't necessarily mean silence or fancy prayers using "thee" and "thou." It may mean raising your hands and shouting praises! But it definitely means a mindfulness of Whose presence you are in. And that mindfulness is not just when we enter the church building. With the Holy Spirit indwelling us, we should be mindful of His Presence always in our life.
On the one hand, because of Jesus' sacrifice for us, God gives us the privilege of being able to approach His throne of mercy at any time, as only the High Priest of the Israelites was able to do, and then only once a year and with the appropriate sacrifices. But God is still God. He is still Holy and Awesome and worthy of our reverence.