A repeated phrase heard in Christendom is that the law is obsolete and therefore non-applicable to New Testament believers.

There's a real problem here: in so stating, we're saying that we are obligated to keep man's law's (with which we comply daily); it's only God's laws that we can excuse ourselves from obeying.

However, the Bible tells us that God's word is eternal and never fails.

"The grass withers, the flower fades,
But the word of our God stands forever." Isaiah 40:8

"The sum of Your word is truth,
And every one of Your righteous ordinances is everlasting." Psalm 119: 160

[See also Psalm 119:158, 133, 105, 101, 89; Psalm 105:8; I Kings 8:56]

The word "law" in Hebrew is torah, meaning the instructions and teachings of God (Yahweh/YHWH). How can God's teaching and instructions be obsolete? Does YHWH change His mind? According to Scripture, He does not. (Malachi 3:6; Hebrew 13:8)

Therefore, how can YHWH's torah be obsolete and no longer apply to us? Where did we get this idea? We got it from a gentile mistunderstanding of something Paul said:

        "14 For He Himself is our peace, who made both groups into one and broke down the barrier of the dividing wall,
15 by abolishing in His flesh the enmity, which is  the Law of commandments contained in ordinances, so that in Himself He might make the two into one new man, thus establishing peace
        16 and might reconcile them both in one body to God through the cross, by it having put to death the enmity."  Eph 2:14-16

What Y'shua put to death on the cross was the enmity* the torah created between those who obeyed it and those who didn't. By being grafted into Israel (Romans 11:11-24; Ephesians 2:12; Galatians 3:29) He removed the enmity as we became a part of them. (...remember that  it is not you who supports the root, but the root supports you. Rom 11:18) As a part of Israel, we are to keep the same torah (instructions) our Saviour did.

Perhaps it's time for believers in Messiah to begin to live like He did: in accordance with YHWH's teaching and instructions instead of excusing ourselves from living in accordance with ALL of YHWH's word.

*enmity - NT:2189 echthra (ekh'-thrah); feminine of NT:2190; hostility; by implication, a reason for opposition:
KJV - enmity, hatred.