I visited at a church of Christ nearby and was thinking about attending there on a permanent basis but I noticed they had a cross painted on a sign in front of the building and a clock in the shape of a cross with a picture of Jesus in the center on the wall. They also had crosses on the communion trays and one on the front of the communion table. What are your thoughts on this subject?
There is no trademark on the name "Church of Christ," so you will find a variety of groups using the name. I don't know which group you visited, so I can't make specific remarks toward their beliefs.
Among the conservative churches of Christ, sometimes referred to as the non-institutional churches, the use of religious symbols is avoided. Though at times this is difficult to do. For instance, most communion trays available for purchase come with crosses on top. Fortunately most are attached with a screw, so we run down to the local hardware store and find a nice knob to use in its place. I once worshiped in a small church that had a cross on its podium. It was given to the congregation and they couldn't afford a replacement, so they put up with it for several years.
As to why it is avoided, the answer is simple: there is no direction by God for the use of religious symbols to adorn meeting places. The symbols that we do have are the Lord's Supper (I Corinthians 11:23-29) and baptism (Romans 6:3-7). Our preachers do not carry special titles to distinguish themselves (Matthew 23:6-12), nor do they wear special clothing to set them apart (Matthew 23:5). For the same reason the members do wear jewelry or items to say "See, here is a Christian." We want to be noticed for who we are, not by what we claim to be (John 5:44; I Peter 3:3-7).
Perhaps in the days when illiteracy was great a need for some icon to mark a place of worship was necessary, but people have a tendency to place significance on man-made symbols. A good example of this was the bronze serpent made by Moses to allow a cure from snake bites (Numbers 21:9). Moses made it at the direction of God and it served its purpose. But centuries later people made an idol out of that same bronze serpent (II Kings 18:4). We see this same tendency today. People treat crosses and other religious symbols as good luck pieces. In some religions people kneel before crosses to offer prayers. Knowing what people tend to do, we choose to avoid the issue.
Worship can take place anywhere Christians are gathered (I Corinthians 11:18; 14:23). It doesn't require the use of man-made symbols. We don't need a building with a steeple or adorned with crosses. I know of congregations that meet around kitchen tables, in garages of homes, in a pavilion at the side of a village, in a renovated auto-repair shop, and in a bay of a shopping center. The importance is placed on Christians assembling together, not on the decorations.