Doing all things in the name of the Lord has no limits (3:17). This even applies to slaves and masters. Slaves obey, and masters show fairness. God's greatest concern in this age is salvation and sanctification, not social reform/justice.[1]
Slaves (3:22-25): Slaves had no freedom or rights,[2] and God's will for them was straightforward: "in all things obey."[3] This is no mere external obedience or mere "eye-service,"[4] but one that's sincere. Believing slaves are not "men-pleasers."[5] Instead, they fear the Lord. They see every task ("whatever you do") as an opportunity to work for the Lord. He is their rewarder, not their earthly masters: "It is the Lord Christ whom you serve." Moreover, in serving the Lord, believers have both a protection and an accountability.[6] As the faithful and impartial judge, the Lord never turns a blind eye to evil.
Masters (4:1): Slaves were considered as property, and masters had legal rights over them. Hence, the masters are called to show justice and fairness, not out of a legal obligation, but for the Lord's sake. The masters, too, have "a Master in heaven." The Lord's rule supersedes any legal right from the state.
[1] Slavery was common in the Bible, both in Israel's history (Gen. 15:13; 47:19; Lev. 25:44; etc.) and in the NT—the church often had saints who were slaves (1 Cor. 12:13; Gal. 3:28; Col. 3:11). At times, God granted relief through emancipation (1 Cor. 7:21), but perfect justice will come in the future kingdom (Isaiah 42:1-4). This passage urges at least one runaway slave to heartily serve his master (4:8-9; Phm. 10-18; 1 Tim. 6:2).
[2] Slaves were legal property to their masters and had
no freedom (a "slave" is one in bondage). Employment is not the same
as this. Christians have the freedom to leave their job. Neither the boss nor
the paycheck nor the project owns them. There is no Biblical basis for
compromising one's obedience to Christ to keep a job.
[3] This command is identical to 3:20: the verb is "obey [hu-pa-kou-e-te (ὑπακούετε)]" and its scope "all things."
[4] The phrase "external service" is literally "eye-service [oph-thal-mo-dou-li-a (ὀφθαλμοδουλία)]" (ESV, NKJV).
[5] "Those who merely please men" is literally "men-pleasers [an-thrō-par-es-kos (ἀνθρωπάρεσκος)]." We are all accountable to the Lord who sees beyond the surface and sees the heart (Ps. 11:5-7; Rev. 2:23).
[6] Paul does not say if the wrong-doer of 3:25 is a slave or a master. Either way, the impartial Judge will deal with every perpetrator. The "consequences" are simply future ("will"). It may be in this life and/or in eternity.