The Dictionary for Theological Interpretation of the Bible highlights the theologians' difficulty in reconciling Galatians, Matthew, and James:
“There are much greater difficulties in plotting the relations between Galatians and works like Matthew and James, which emphasize performing works of the law and doing all that Jesus commanded. Certainly Luther felt that it was not possible to reconcile Paul and James, which he famously dismissed as an “epistle of straw,” just as commentators have continued to see Matthew’s emphasis on judgment by works as inimical [harmful] to Paul’s teaching...”
Such reconciliation difficulties aren't inherent in the texts themselves. For all three books teach “Love your neighbor as yourself” as the entire Law and as the entire Judgment Day standard — including Paul:
"the entire Law is fulfilled in one utterance, 'Love your neighbor as yourself.'... Fulfill the King's Law by bearing one another's burdens.... he who sows in the Spirit shall reap the Spirit’s immortality. When we are doing something benevolent, let's not do it half-way because we will reap [immortality] at the proper time if we're unrelenting." — Galatians 5.14, 6.2, 8-9
Matthew taught the identical concept [Matthew 19.16-19] and James did as well [James 2.8-13]. All three books taught the same Law and the same judgment standard. Thus, for denominations which teach brotherly love as the entire Christian ethic, there's nothing to even reconcile.