"Christ also has suffered once for sins, the Righteous on behalf of the unrighteous, that He might bring you to God, on the one hand being put to death in the flesh, but on the other, made alive in the Spirit; in which also He went and proclaimed to the spirits in prison, who had formerly disobeyed when the long-suffering of God waited in the days of Noah, while the ark was being prepared; entering into which, a few, that is, eight souls, were brought safely through by water. Which water, as the antitype, also now saves you, that is, baptism, not a putting away of the filth of the flesh but the appeal of a good conscience unto God, through the resurrection of Jesus Christ." - 1 Peter 3:18-21
Can this phrase from 1 Peter 3:21 be translated as "the request addressed (by God) to a good conscience in God." meaning that God demands baptism from every man who has a good conscience in God.
I'd say no since the subject there is baptism, which is the believer's act toward God, not God's action or request toward the believer.
As far as what the verse means affirmatively, Thayer's comment seems most true. Baptism is a believer's request or appeal to God. For salvation. Not salvation from eternal condemnation, since baptism has nothing to do with that (Mk 16:16). But salvation from "Pharaoh" (Satan) and the world (Ex 14:30; Heb 11:28-29). Nor salvation from the sin in our flesh, the "filth" (Jam 1:21; 1 Jn 1:8), since only the experience of Life (Christ) rescues us from that (Rm 8:2). This also annuls the ignorant or evil teaching of "infant baptism." Since baptism is of volition and faith. Of the baptized one. Not of a third party's faith or will. Baptism could be said not to be a "sacrament" since, in Scripture at least, there is no such thing as sacraments - that is, inanimate impersonal things infused with God or grace to, in effect, serve as idols or talismans. Peter says "water" then clarifies that to mean baptism.
The word might also be translated "answer" of a good conscience to God, since God commands baptism after faith (Ac 8:36) and baptism is the obedient response to God's command. "Examination" is okay, since it suggests an inquiry which resembles a request or appeal, but the English becomes unnecessarily bulky, and also lessens the directness of the interchange. Baptism (immersion in water) is simple and evocative (of death and entrance into), and is a visible act. Not a thought or invisible choice.