If the lexicon had not said "sincere" as a choice of translation, or if it is not considering "sincere" as having the etymology or definition you are using, then is there the same problem with the Greek word? Here are 3 lexicons (highlighting is mine) and we can see in the Greek that it goes back to Greek drama and "play-acting" - the hypocrite - and it mainly means "pretense" which is also an English definition for "sincere".
Bauer-Danker, Greek-English Lexicon of the NT (BDAG)
[BDAG] ἀνυπόκριτος
• ἀνυπόκριτος, ον (s. ὑποκρίτης; schol. on Aristoph., Av. 798; Iambl., Vi. Pyth. §69, 188 αἰδώς; Ps.-Demetr., De Eloc. 194; Wsd 5:18; 18:15) pert. to being without pretense, genuine, sincere, lit. ‘without play-acting’ ἀγάπη (ApcSed 1:4) Ro 12:9; 2 Cor 6:6. φιλαδελφία 1 Pt 1:22. πίστις 1 Ti 1:5; 2 Ti 1:5. σοφία Js 3:17.—DELG s.v. κρίνω. M-M. TW. Spicq.
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Liddell-Scott, Greek Lexicon (Abridged)
[LS] ἀνυπόκριτος
ἀν-υπόκρι²τος, ον, (ὑποκρίνομαι) without dissimulation, N.T.
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Louw-Nida, Greek-English Lexicon of the NT
[LN] ἀνυπόκριτος ον genuine 73.8
Isn't pretend faith also false faith - pretending to believe something?