What that verse is talking about is pursuing the kingdom of God.
Here is the thing, we are commanded to love all men, including our parents:
Let no debt remain outstanding, except the continuing debt to love one another, for whoever loves others has fulfilled the law. - Romans 13:8
We are also commanded to honor our parents:
Honor your father and your mother, so that you may live long in the land the LORD your God is giving you. - Exodus 20:12
But when we review love in 1 Corinthians 13, we learn that love rejoices in the truth!!!
A disciple of Christ, stands on the truth of God's word and standing on this truth, may cost you family members and you have to be willing to pay that cost:
Matthew 10:34-35 - Do not suppose that I have come to bring peace to the earth. I did not come to bring peace, but a sword. For I have come to turn "'a man against his father, a daughter against her mother, a daughter-in-law against her mother-in-law--
The sword Christ brought is his word, which is a sword. That sword divides families over the gospel.
But you see, if you fellowship with your family as believers of Christ, then what happens is you are united in the spirit of Christ, and this is good and God approves of it if done according to the word.
In my situation my parents are either lost, or might as well be in terms of their life. I see them often but I have "lost them" in the sense that the new person I am has nothing to do with who they are. I can minister to them out of love, but there is no longer fellowship between me and them. I cannot fellowship with the world.
They are not offended because they don't understand... but when they make world comments, I don't agree. When they have unbelief in God, I don't agree. And since they offer nothing of Jesus Christ, there is no agreement. There is no bond of love between us, because lost people can't love, they haven't received God's love in that they might love.