Justo Gonzalez in his survey of church history writes, "While all [apologists] agreed on the need to abstain from idolatry, not all agreed on what should be a Christian's attitude to classical pagan culture." Some believed that to reject all of it would be tantamount to rejecting some of the highest intellectual achievements of the day. This was especially true of the great philosophical thought of Plato, Aristotle, and the Stoics. (It would not take long before philosophy, especially that of the Platonic school, became the framework in which theology was performed.) Others felt that to accept such thought was to make concessions to paganism. This could bring about idolatry.
Therefore, the apologists took one of two approaches. Some insisted on a radical opposition between Christianity and pagan culture, including philosophy (e.g. Tertullian, b. 150 AD). Others saw many complimentary connections between philosophy and Christianity (e.g. Justin, 110-165 AD).
The apologists also addressed Christianity's relationship to Judaism. The core question was, "Who are the true heirs of the covenant?" Justin wrote a treatise addressed to Trypho, a rabbi (Dialogue with Trypho). The Dialogue claims to be the record of a conversation between Justin and Trypho concerning the correct interpretation of the Old Testament. Justin declares that there is a new priesthood that has replaced the old one. Christianity is the new priestly race (Dialogue, 116).
It is important to say that few apologists addressed Judaism in a serious way. Justin, and later Origen, were two of the few who did so. After Jerusalem was destroyed in AD 70, Jewish polemic against Christianity became increasingly defensive (for good reason) which was a shift from earlier years. Christian thinkers began to feel more comfortable in developing their their thought without engaging the rabbis. Christians began to see the Hebrew Scriptures as their own. One of the unfortunate results was that they no longer gave serious consideration to Jewish interpretation of the Old Testament nor the Jewish context of the New Testament.
The resultant anti-semitism that would spring from this reading of Scripture and understanding of Christianity in the church down through the centuries would have devastating consequences.
A Weblog Dedicated to the Discussion of the Christian Faith and 21st Century Life
I do not seek to understand that I may believe, but I believe in order to understand. For this also I believe, –that unless I believed, I should not understand.-- St. Anselm of Canterbury (1033-1109)