Does discipleship overrule responsibilities to the family?

Considering Luke 14:26, does discipleship conflict with family responsibilities?

Disciples must obey "whatsoever I have commanded you" (Matthew 28:20). Paul states that his writings are "the commandment of the Lord" (1 Corinthians 14:37). Therefore, Paul’s teaching that children obey their parents (Ephesians 6:1), that husbands love, cleave to, cherish, and nourish their wives (Ephesians 5:28-31), that parents provide for their children (2 Corinthians 12:14), and that all manifest the affection of brotherly love (Romans 12:10) cannot conflict with Christ’s requiring His disciples to hate their father, mother, wife, children, brothers, and sisters.

Luke’s record of the Lord’s previous use of the word "hate" is in 6:27, where we are to love and express good will even toward those who hate us. Therefore Luke 14:26 cannot teach absolute hatred toward our closest relatives when we are to love even our enemies. The Lord’s next use of "hate" (16:13) pictures a servant with two masters. If both give him a command, his response will involve either love, holding to one (same word as "holding fast" the faithful word, Titus 1:9), or hate, being heedless (YLT) of the other. Loyalty and its resulting obedience are the issue. This is relative hatred. The demands of our dearest cannot rival our loyalty and obedience to Christ. The security and comfort of cherished relationships cannot compromise our commitment to Christ. But let us be assured that to act in loyalty to Christ is to do what is absolutely best for our loved ones.

D. Oliver