The answer to your question hinges on a controversy among Greek grammarians and lexicographers.
Thayer, in his Greek/English lexicon does not accept the causal use of 'eis'; but, Bauer, Arndt, and Gingrich do in theirs.
A.T. Robertson, among others concurs in accepting the causal use of 'eis'.
If we translate Acts 2:38
Believe, and be baptized because your sins are forgiven; the question disappears.
I believe that this is the correct translation.
As is seen on the title page, Thayer’s Greek Lexicon is the English translation of Grimm’s Wilke’s
Clavis Novi Testamenti. The
Clavis Novi Testamenti is a two-volume work, the second edition of which was published in 1851. Thayer finished his translation of this two-volume lexicon on Christmas day, 1885, but it soon became obsolete with the publication (1901-1910) of the research by Gustav Adolf Deissmann on the papyri discovered in Egypt. Indeed, it was this research that established that the New Testament was written in Koine Greek rather than a special Greek dialect found only in the New Testament.
By the early 1900’s, the new studies in the lexicography of Koine Greek had become so great in number and significance that Erwin Preuschen published his Greek-German lexicon in 1910. Upon his death in 1920, the revision of his lexicon was entrusted to Walter Bauer and this revision was published in 1928 as the second edition. In 1930, James Hope Mouton and George Milligan independently published
The Vocabulary of the Greek Testament. A thoroughly revised edition of the Preuschen lexicon was published in 1937 with only Bauer’s name on the title page. Bauer realized, however, that his lexicon, although a huge improvement over Thayer’s in terms of accuracy and completeness, needed to be thoroughly revised and updated and therefore undertook a thorough search of all Greek literature down to the Byzantine times to determine more precisely the meaning of the words found in the New Testament. This resulted in the publication of the monumental work,
Griechisch-Deutsches Wörterbuch zu den Schriften des Neuen Testaments und der übrigen urchristlichen Literatur in 1949-1952. An English translation (by William F. Arndt and F. Wilbur Gingrich) of this lexicon was published by the University of Chicago in 1957 with the title,
Greek-English Lexicon of the New Testament and other Early Christian Literature and became widely known as the “Bauer, Arndt, and Gingrich Lexicon.” A second edition was published by the University of Chicago in 1979. A thorough revision by Frederick William Danker was published by the University of Chicago in 2000. It is very commonly referred to simply as the “BDAG” and this name appears on the title page in parenthesis below the full title.
On page 290 of the BDAG we read that, in regard to the Greek preposition εἰς, in Acts 2:38 it is used “to denote purpose… so that sins might be forgiven”, as in Matt. 26:28, Mark 1:4, and in Luke 3:3.
Therefore, the correct translation of Acts 2:38 is,
Acts 2:38. Peter said to them, “Repent, and be baptized every one of you in the name of Jesus Christ so that your sins may be forgiven; and you will receive the gift of the Holy Spirit.” (NRSV)