NIV 1 Corinthians 10:1 For I do not want you to be ignorant of the fact, brothers and sisters, that our ancestors were all under the cloud and that they all passed through the sea.
No. Better reading is in Young's:
"And I do not wish you to be ignorant, brethren, that all our fathers were under the cloud, and all passed through the sea,"
Have to consider the new status under the gospel of Christ, that all who are in Christ and covered by His blood are counted for the seed of Abraham, and are therefore Israel. By God's definition, being counted for the seed of Abraham, all Christians, Jew and Greek are spiritual Jews, circumcised of the heart (Rom. 2:29; Gal. 3:26-29).
Corinth was in the Peleponnese, in south central Greece. Most probably, there were a mix of Jews and gentiles (nations) at the church of Corinth. The letter was sent to Christians (1 Cor. 1:1-2), and as all Christians of all nations are grafted into the branch (Rom. 11:17-24), then those of the old covenant congregation are "our fathers," too.
If you are interested, I have two posts at my site on the change in the definitions that took effect under the new covenant: God's Definitions - Part I: The House of Israel, and - Part II: The House of God. See ShreddingTheVeil.