Because of Christ, the ceremonial law is repealed.
Because of Christ, the church is no longer a nation-state imposing civil penalties.
It all falls into place. However, if you reject the idea of Christ as Son of God and Savior, then, of course, the Bible is at best a mish-mash containing some inspiration and wisdom, but most of it would have to be rejected as foolish or erroneous.
So where does this leave us? There are only two possibilities.
If Christ is God, then this way of reading the Bible makes sense and is perfectly consistent with its premise. The other possibility is that you reject Christianity’s basic thesis—you don’t believe Jesus was the resurrected Son of God—and then the Bible is no sure guide for you about much of anything.
But the one thing you can’t really say in fairness is that Christians are being inconsistent with their beliefs to accept the moral statements in the Old Testament while not practicing other ones.
One way to respond to the charge of inconsistency between the Old Covenant and the New may be to ask a counter-question: “Are you asking me to deny the very heart of my Christian beliefs?” If you are asked, “Why do you say that?” you could respond, “If I believe Jesus is the the resurrected Son of God, I can’t follow all the ‘clean laws’ of diet and practice in the Old Covenant, and I can’t offer animal sacrifices. All that would be to deny the power of Christ’s death on the cross. And so those who really believe in Christ must follow some Old Testament texts and not others.”