At the beginning of our conversion, usually during counseling for baptism, we are asked to consider this passage seriously. Verses 26-27 are particularly important because loyalty to Christ is the issue in this context. Jesus makes it plain that, after entering into the New Covenant, our highest loyalty is to Him.
This is extremely important because the character of every life is determined by the loyalty that rules it. Peter confirms Jesus' words in Acts 5:29, saying, "We ought to obey God rather than men." He made this affirmation following Jesus' crucifixion. Persecution was imminent against the fledging church. However, we must understand that the world is always a threat against our loyalty to Christ. Life is a mixture of choices and compulsions, and many of our values have their source in the world. These values exert an ever-present pressure to conform to them, thus we must be aware.
The pressure to make moral choices is the furnace in which character is forged. Our compulsions to make choices come in two varieties: 1) forced, as by a gun to our temple that demands, "Do this or else," and 2) unforced, the pressure of old habits, perspectives, and attitudes engraved in our character, hangovers from our past. Thus, the past and the present both push at us to choose. What we choose determines where our loyalties lie and thus whether we commit idolatry. If we are not thinking carefully, idolatry is an easy sin to fall into.