Godliness does not necessarily mean what we tend to think of
the greek word means "devout"
The word eusébeia literally means well-directed reverence, but does not imply an inward, inherent holiness. It is actually an externalized piety. Paul uses it only in the pastoral epistles....
When Paul came to Athens and spoke to the Athenians who certainly were not believers, but worshiped idols, he used the verb eusebeíte (G2151), to show piety, respect (
Act_17:23). An unbeliever in the NT may be eusebḗs, pious, or may be asebḗs (G765), impious. However, neither condition is díkaios (G1342), righteous, just, nor dikaiōthḗs (G1344), one justified or having God's righteousness imputed to him by Jesus Christ, nor pistós (G4103), a believer who is characterized by the exercise of pístis (G4102), saving faith in the person of the Lord Jesus Christ. On the other hand, the opposite of eusébeia is asébeia (G763), ungodliness, or, better still, impiety. ...
The Complete Word Study Dictionary
NET bible commentary. Grk "great is the mystery of [our] religion," or "great is the mystery of godliness." The word "mystery" denotes a secret previously hidden in God, but now revealed and made widely known (cf.
Rom_16:25; 1Co_2:7; 1Co_4:1;
Eph_1:9;
Eph_3:3;
Eph_3:4;
Eph_3:9;
Eph_6:19;
Col_1:26-27;
Col_4:3). "Religion" (εὐσέβεια, eusebeia) is a word used frequently in the pastorals with a range of meanings: (1) a certain attitude toward God-- "devotion, reverence"; (2) the conduct that befits that attitude-- "godliness, piety"; and (3) the whole system of belief and approach to God that forms the basis for such attitude and conduct-- "religion, creed." See BDAG 412-13 s.v.; 2Ti_3:5; 4Ma_9:6-7; 4Ma_9:29-30; 4Ma_15:1-3; 4Ma_17:7. So the following creedal statements are illustrations of the great truths that the church is charged with protecting (1Ti_3:15).
Robertson's Word Pictures
The mystery of godliness (to tēs eusebeias mustērion). See 1Ti_3:9 “the mystery of the faith,” and 1Ti_2:2 for eusebeia. Here the phrase explains “a pillar and stay of the truth” (1Ti_3:15). See in particular 1Co_1:27. “The revealed secret of true religion, the mystery of Christianity, the Person of Christ” (Lock).