A brief comment.
1. It is an announcement. It is public.
The Holy Supper, or Supper of the Lord, commemorates Christ and His sacrifice made once and for all for a complete and final remission of sin.
It is to profess publicly that "the Lord died for me".
2. Jesus said:"This IS my flesh", referring to the bread He held in His hand. "This IS my blood", referred to the wine in the cup.
Since none of the two elements were His flesh or His blood, we understand them to be symbolic elements. It was the symbolism of the work of Jesus: some time later He would give His body to be torn and His blood was shed, and it was for us.
The fact that we not only announce the death of the Lord with that Supper, but also that we eat and drink the symbols of it, was something formerly only understandable to the Jews, who were accustomed to such feasts after the atonement sacrifices, and they did it with the meaning of a personal appropriation of the benefits of that offering.
3. One should not participate "unworthily".
The primary warning was toward the irreverent way in which they participated of this symbol.
In those days it was common to dine together and to -at the end of the meal- participate of this commemoration, or to remember what Jesus had done.
There were some who not even stopped to meditate on it. In others, with sin in their hearts, there was neither remorse nor repentance for their sins, and they pretended by means of a natural action, with that "fulfilling" of the remembrance, to consider the sin as cleansed, without going through the true cleansing.
The external acts don't solve the internal.
A proper approach to the remembering of His work adds the examination of oneself, especially in those moments of commemoration. Because what is remembered is that Christ gave His flesh and His blood for our sins against God.
And, by extension, the love of God in sending His Son on our behalf is also remembered, all of which should take away all iniquity in our drawing near.
To examine oneself (the Scripture also says "judge") should not be interpreted as for a final purpose as within a trial, which is to emit sentence, to condemn. We are not called to "condemn ourselves" by our sinful deeds, but to "judge ourselves" and with the results of our judgement, to draw near to Him.
What is suggested is to participate of the Holy Supper with the circumspection it deserves. The self-examination is not with the end of leaving the table, but with the purpose of participating of it.
Yet, within this examining is also included our relationship with our neighbour, whether he be a brother in the faith or not.
5. Discerning "the body of the Lord".
The work of Jesus embraces all the redeemed, who are His Body.
Nevertheless, the "unworthily" mentioned in 1 Co 11:27 is defined in Greek as "not discerning the body of the Lord" in the symbols, not in the relationship between brethren.
6. The Body. The Church.
While Paul mentioned the unworthiness of some who drew near to the Holy Table, the real situation was not unknown to him: dissensions, divisions, schisms, caused by opinions, by affinity with Paul or with Apollos, or by the importance some gave to certain gifts minimizing others.
When Paul warned about the manner of approaching, it possibly was in response to open actions related to the existing disagreements that were expressed during the moments of the participation. The very same ordinance established for the unification of the believers into one body was occasion for divisions.
To hold different opinions does not seem to affect the participation of the Holy Supper. But the lack of love certainly does not belong there.
One same and only work of Christ is for all of us sinners. Respect, order, harmony and love during that remembrance must predominate between those who long after the holiness and love that come through the regeneration by the Holy Spirit.