By the introduction we can see that Paul is writing to those in the church at Corinth and all those who in every place call on the name of the Lord Jesus (1 Cor.1:2). The Jews who lived in every place called on the name of the Lord Jesus so when Paul wrote this it was addressed to the Jewish believers in every place:
"For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ. For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit" (1 Cor.12:13).
Cornelius Stam, the founder of the Berean Bible Society, wrote the following commentary on 1 Corinthians 1:2:
"There are other evidences that the kingdom saints of Paul's day became members of the Body of Christ. In I Corinthians 1:2, Paul addresses his letter to the Corinthian church, 'with all that in every place call upon the name of Jesus Christ our Lord, both theirs [those in every place] and ours [those with Paul].' And he says to 'all' these believers 'in every place': 'For by one Spirit are we all baptized into one Body, whether we be Jews or Gentiles' (I Cor. 12:13). How can this be made to exclude the Judean believers?" (Cornelius Stam, Commentary on Galatians [Stevens Point, WI: Worzalla Publishing Co., 1998], 198).
Cornelius Stam is not alone about his interpretation of 1 Corinthians 1:2. Matthew Henry wrote:
"In conjunction with the church at Corinth, he directs the epistle 'to all that in every place call on the name of Christ Jesus our Lord, both theirs and ours' " (Matthew Henry, Commentary at 1 Corinthians 1:2).
John Nelson Darby understood the verse in the same way, writing the following:
"He addresses the assembly of God at Corinth, adding a character (the application of which is evident when we consider the contents of the epistle) 'sanctified in Christ Jesus.' Afterwards the universality of the application of the doctrine and instructions of the epistle, and of its authority over all Christians, wherever they might be, is brought forward in this address" (John Nelson Darby, Commentary at 1 Corinthians 1:2).
A.R. Fausset comments on the verse matches the commentary of both Stam and Darby:
"with all that in every place call upon . . . Christ--The Epistle is intended for these also, as well as for the Corinthians. The true CATHOLIC CHURCH (a term first used by IGNATIUS [Epistle to the Smyraeans, 8]): not consisting of those who call themselves from Paul, Cephas, or any other eminent leader ( 1Cr 1:12 ), but of all, wherever they be, who call on Jesus as their Saviour in sincerity (compare 2Ti 2:22). Still a general unity of discipline and doctrine in the several churches is implied in 1Cr 4:17 7:17 11:16 14:33, 36" (A. R. Fausset, Jamieson, Fausset & Brown; Commentary on 1 Corinthians 1:2).