No, a church should not require its members to take communion. There might be times in the Christian's life where he is in sin to such a significant degree that it it would be advisable to not take communion. Let's take for example that a person is committing adultery, knows it is wrong, but is continuing to do so. Such a person should not take communion because he is not in a state of repentance or struggle against his sin. Furthermore, if the church were to require such a person to take communion, it could potentially cause the person to do so in an unworthy manner.
1 Cor. 11:26-29 says, "For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until He comes. 27 Therefore whoever eats the bread or drinks the cup of the Lord in an unworthy manner, shall be guilty of the body and the blood of the Lord. 28 But let a man examine himself, and so let him eat of the bread and drink of the cup. 29 For he who eats and drinks, eats and drinks judgment to himself, if he does not judge the body rightly."
Also, since communion is meant only for true believers who have repented of their sins, and since some churches are so liberal that they are not really Christian and even encourage sin, requiring a person to take communion would essentially amount to a sinful act.