According to some Reformed theologians (e.g., Charles Hodge; Joel Beeke), as the Greek New Testament never uses the words δια πιστεως ("through faith") in the accusative form which would denote causality ("because of faith"), only in the genitive, one's righteousness is not "because of" or "on account of" one's faith. According to Joel Beeke, the accusative δια την πιστιν would convey the notion of "on the ground of" faith, thereby making faith the meritorious reason for the believer's acceptance of God.
The contention of Hodge, Beeke, and others fail when examined carefully. Among the problems with this linguistic trick by Protestants, one should note the following:
Firstly, there is a confusion between the meritorious cause and the instrumental cause of salvation. In LDS theology, it is the atoning sacrifice of Christ that is the meritorious cause of salvation; faith (as understood by LDS theology) is not the meritorious cause, but an instrumental cause.
Secondly, δια is used in the accusative case in reference to faith. For example, in Hebrews 3:19, we read:
καὶ βλέπομεν ὅτι οὐκ ἠδυνήθησαν εἰσελθεῖν δι᾽ ἀπιστίαν
So we see that they were unable to enter because of unbelief. (NRSV)
This should be compared with Heb 4:6:
ἐπεὶ οὖν ἀπολείπεται τινὰς εἰσελθεῖν εἰς αὐτήν, καὶ οἱ πρότερον εὐαγγελισθέντες οὐκ εἰσῆλθον δι᾽ ἀπείθειαν
Since therefore it remains open for some to enter it, and those who formerly received the good news failed to enter because of disobedience (NRSV)
In these texts, we learn that the Jews of the Old Testament received the gospel (cf. Heb 4:2) but were not blessed by God and thus understand divine judgement because of (δια in the accusative) their disbelief (απιστιαν) and disobedience (απειθειαν) (cf. 1 Cor 10:1-12).
Other texts that use δια in the accusative in relation to faith include:
And he did not many mighty works there because of their unbelief (διὰ τὴν ἀπιστίαν αὐτῶν) (Matt 13:58)
And Jesus said unto them, Because of your unbelief (διὰ τὴν ὀλιγοπιστίαν ὑμῶν): for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you. (Matt 17:20)
While δια in the accusative case is never again used with “faith” in the Greek New Testament, what is often overlooked is that δια in the accusative case are never used of any act of redemption in the New Testament, including the meritorious cause of justification (the atonement of Christ). Δια in the accusative case is used only in reference to non-redemptive acts (e.g., Rom 2:24; Phil 1:24; Jas 4:2).
The New Testament authors have a preference to use δια in the genitive case, including the atonement of Christ, the meritorious cause of justification (e.g. John 1:7; Acts 3:16; 10:43; 15:11; Rom 5:5, 9, 10, 17, 21; Heb 2:14; 1 Pet 1:3; 3:21).
Finally, only three verses even remotely speak in redemptive terms using δια in the accusative case (2 Cor 9:14; Eph 2:4; Heb 2:9), but none of these texts speaks of the cause of justification as the imputation of the alien righteousness of Christ.
On the topic of the preposition δια and its importance towards Christology, particularly the personal pre-existence of Jesus, see Thomas Farrar (ex-Socinian [Christadelphian]), The Greek word dia: A little word with big Christological implications