"As a precautionary measure, Paul wisely advised Timothy to be circumcised—not that God required it, but in order to remove from the minds of the Jews that which might be an objection to Timothy's ministration. In his work Paul was to journey from city to city, in many lands, and often he would have opportunity to preach Christ in Jewish synagogues, as well as in other places of assembly. If it should be known that one of his companions in labor was uncircumcised, his work might be greatly hindered by the prejudice and bigotry of the Jews. Everywhere the apostle met determined opposition and severe persecution. He desired to bring to his Jewish brethren, as well as to the Gentiles, a knowledge of the gospel, and therefore he sought, so far as was consistent with the faith, to remove every pretext for opposition. Yet while he conceded this much to Jewish prejudice, he believed and taught circumcision or uncircumcision to be nothing and the gospel of Christ everything. AA 204.1"
"And unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law;"
The EGW passage explains Paul's decision to have Timothy circumcised to avoid hindering his ministry among the Jews, emphasizing Paul's willingness to adapt to cultural sensitivities for the sake of the gospel. This aligns with the principle expressed in 1 Corinthians 9:20, where Paul states he became as a Jew to win the Jews. The core idea of adapting to the audience to facilitate the spread of the gospel is present in both.
"Paul loved Timothy, his “own son in the faith.” 1 Timothy 1:2 . The great apostle often drew the younger disciple out, questioning him in regard to Scripture history, and as they traveled from place to place, he carefully taught him how to do successful work. Both Paul and Silas, in all their association with Timothy, sought to deepen the impression that had already been made upon his mind, of the sacred, serious nature of the work of the gospel minister. AA 204.2"
"Unto Timothy, my own son in the faith: Grace, mercy, and peace, from God our Father and Jesus Christ our Lord."
Ellen White directly references 1 Timothy 1:2 in this passage.