Specifically, do you think atheists should participate in communion if they happen to be attending a church? Remember that nobody's brain is 100% belief or 100% disbelief. If a person like myself is baptized but now is 99% disbelief, I wonder what is appropriate? Personally, I think that an atheist should participate, because denying people access to Jesus contradicts the behavior of Jesus in the gospel. Jesus repeatedly went to the people that society was rejecting.
It depends on who you are asking.
There are denominations that take the position you mention, for the reasons you mention.
However ... we take great care in Orthodoxy with receiving the Eucharist, because we know that in the early Church, some people (who were Christians and part of the Church) got sick or even died because they were careless in how they received it. How can we expect someone who doesn't understand or believe in what he is doing not to be in possible danger? When we ourselves receive communion, we fast first, we pray in preparation, we take care to see that there are no sins between us and the Lord, or between us and others. These things might not be possible, or be understood, by unbelievers.
So I would say that no, you should not receive communion in our Church. But not because we wish to exclude you or keep God from you. Rather to protect you from presumption.
It brings to mind an aspect of prayer. Sometimes we as Christians feel that God is distant when we pray, and we may wish for the comfort of His Presence. But the truth is that sometimes we are not in a state to receive Him, and it is a mercy that He does not come to us. But this is more a concern for those who know Him, have grown close, and have a higher degree of accountability. Those who call on Him and meet Him, not knowing Him much or at all yet, can be in a much worse spiritual state, and not suffer for it, because He is merciful and knows our weakness, and protects babes in the faith.
But with what we know of Holy Communion, it is safer to protect people from it. We believe that there are physical and spiritual effects of receiving God Himself into ourselves, and we hope it to be for strengthening, healing, and eternal life - not for condemnation.