I think that’s a false dilemma. You can allow people to attend without making them official members. You can also attempt to spread the Word to these people without requiring that they become members first.
Bolding mine.
You may owe someone an explanation for that. Holy Communion should not be taken in many churches without an true faith in God and acceptance of Christian moral teaching. However, you did say you ahd talked to your priest, so I hope you have listened to whatever he had to say in the matter.
Of course, to an atheist Communion is just a cracker and sip of bad wine.
The interesting thing to me is the acceptance of the church as political animal. It’s no secret that congregations here wield enormous political power, in some circumstances some of the megachurches walking right up to the line and saying “I’m not going to tell you who to vote for this Monday, but you know who God wants you to vote for, wink wink.” It’s just as true on the state and local level as well, some of the biggest political figures here are affiliated with some of the biggest congregations. If you’re running for public office, a congregation is a source of votes, campaign funds, and like-minded individuals in varying positions of political and/or financial power. If your world view is essentially athiestic or agnostic, that’s a closed door for you, and if enough congregations hold political viewpoints antagonistic to yours (or to your thinking outright dangerous), then organized religion is a big problem.
Jensen seems to be saying that if there are religious organizations wielding power that have views antagonistic to my own, it makes sense to ally myself with a religious organization with views compatable with my own, in essesnce saying “I agree with you people on all points except the one metaphysical question that most folks feel is why you all hang out in the first place.” I can see people viewing that as either practical and forward thinking or as a cynical sellout.
In Texas, they’re a downright anomaly! 
Good! You are a brave soul. And I think if you study a little you will find that there is a lot of history in the Bible. Not everything is history but there is some good history there.
I think atheists are downright silly half the time. I think the my alma mater’s football team sucks. I think I vote Republican because the Democrats can’t run someone I would pee on to put out a fire on them.
And I think that if I went to another congregation which I was not actually a part of in truth, I would respect their rules even if they served Ritz crackers and beer.
The bread and wine taken are (depending on the denomination) either physically transformed, or at the very least symbolicly transformed (with degrees inbetween), into the body and blood of Jesus. This transformation only happens for those who have accepted Jesus. A non-believer could only get bread and wine out of it (or beer and crackers). The statement is it’s basically useless from a spiritual standpoint for a non-believer to take communion, sure there are social and physical reasons, but again we are just talking about a few calories.
No, it’s not true of many (if not most) mainstream denominations. Those terms are not usually interchangeable.
As I would use the terms, and have always heard the terms used, “becoming part of the body of Christ” roughly means becoming a Christian. “Joining a church” on the other hand refers to the person’s relationship with a specific congregation (e.g., the one on 3rd and Main).
For most churches, their membership is a small subset of the body of Christ. (There are very few that believe their specific church’s membership is the entirety.)
I know what you say is commonly believed and misunderstood by even many church goers, but it is not the case. As you pointed out a follower of Christ is a ‘Christian’, but when 2 or more are gathered in Christs name this is a part of His church, there is only a single church.
That’s fine. On the rare occasion I do attend church it’s usually because of an event involving a family member. I don’t take communion even though I certainly could walk up there, take a wafer and a sip and head back to the pew without fear of being struck by lightning. My reasoning is to make the point that I’m not back in the religion; my presence is out of respect for my family but I’m not a believer, so I don’t actively participate.
If I enjoyed the music and the social aspects of going to church, believer or not, I could see attending. A few hymns are nice but not enough to make me want to go and I can socialize plenty outside the church. Others can and should do as they please.
And I think we’re going to have to agree to disagree - because from my point of view, you’ve conflated two ideas, “the church” as a whole, and “a church” as a subset congregation or building.
While I am part of the church as a whole, I’m not a member of (to pick at random) “Second Baptist Church of Houston” - I’ve never even been to Texas.
I think athiests should not join churches or attend church services generally, because Churches and religion are harmful and doing so tends to confer credibility on them. Sam Harris explores this point in great detail.
As to whether a church should admit athiests, and noting some of the definitional problems above, I think the questions a weird one. Churches shouldn’t do anything. They shouldn’t even exist. But given that one exists, I think it’s fine for them to “admit” athiests if doing so is consistent with whatever promises they may have made their members or others.
I wonder who appointed you judge and jury of churches?
Same sort of person who appointed you judge and juryof science?
Any thought on know thy enemy? Do you think churches should be monitored by athiests - just to make sure they are not planning something ‘bad’?
Atheists should play golf on Sunday. It is one of the benefits of atheism.
If things are being openly talked about in a (larger than family) church, I would bet on two things; it’s either not bad, or there’s nothing we can do about it.
I should have specified that I attend an Episcopal church; we call ourselves Catholic Lite – all the forgiveness, only half the guilt. 
On a more serious note, I don’t recall any stories about Jesus refusing to minister to anyone who came willingly to him, whether they believed or not. He even loved Thomas; could he love me any less? If you believe Jesus really existed and really did at least something akin to what is related in the Gospels, then how can you refuse to accept me if I come willingly into church? What if my path to salvation is through Holy Communion? Are the Bread of Life and the Cup of Salvation only for those who pass your rigorous standards of faith? It doesn’t matter – I don’t go to your church so it doesn’t concern you.
I can understand not making a statement of faith if you don’t believe something to be true. But a church’s position on theological questions can sometimes be more flexible.
My denomination is small (less than 100,000), but about two hundred years old. During that period, the main book of church doctrine has been rewritten twice. Two of the people who were selected to the committee to rewrite the book are known to me personally. Neither of them agrees with the doctrine completely as it was written. Nor does any one person I know.
Nevertheless, your caution says a lot about your integrity.