At the end of the section of his letter to the Corinthians dealing with "the Lord's table", Paul wrote: "Therefore, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord" (1 Cor 11:27).
What is it to eat in "an unworthy manner"? Some Christadelphians have used this verse to defend their idea of "guilt by association" and as a reason for denying the bread and wine ('Communion') to people who do not share the same doctrinal distinctives, and even to other Christadelphians who disagree on doctrinal details.
In the context of the Corinthian division between rich and poor (see previous message) it seems certain that in Paul's mind to eat or drink "in an unworthy manner" would be to do so in such a way that our Lord's teachings about bringing together all classes and types of people (characterised by His pattern of 'table fellowship') were ignored. The Corinthian rich treated the poor with contempt, and so their meal was 'not the Lord's supper' according to Paul.
Any religious service, regardless of whether or not 'Communion' or 'breaking of bread' is a feature, if it flies in the face of our Lord's inclusiveness by denying participation to any member of the Body of Christ, is 'not the Lord's supper'. There is no reason to think that a mere token consumption of a morsel of bread and a sip of wine is 'the Lord's Supper', especially if it is based on exclusivism and denies access to anyone.
In fact, those Christadelphians who are exclusive in their fellowship practices may themselves be guilty of eating and drinking "in an unworthy manner". To celebrate breaking of bread "without recognizing the body of the Lord" is to bring judgment on ones self. Paul is saying that those who are 'in Christ' are the body of Christ and must be treated in love.