A realist ontology -- one which posits real knowledge of being in itself -- will correspondingly imply a realist theological stance, and likewise a nonrealist ontological stance will imply a nonrealist theology. In other words, if we believe that we can know things in themselves, then we will be inclined to take theological statements as real and adequate descriptions of God's being in himself. On the other hand, if we have doubts about the possibility of knowing being in itself, then we should likewise be skeptical that theological statements describe God's actual being.
I go back and forth between these extremes. Some days I am inclined to take theological statements such as the presence of Christ in the Eucharist, union with Christ, etc., as real statements of metaphysical facts. Other days I am inclined to think of these as endorsed ways of conceiving of the world, which are spiritually useful insofar as they form us and train us to think and feel certain ways, but which may not be the fact of the matter; the fact of the matter would be unknowable. It is hard for me to come down on one side.
I think there is a problem with taking some theological statements in a realist way. For instance, Paul tells the Corinthians not to consort with prostitutes, and he appeals to the doctrine of union with Christ: Do you not know that your bodies are members of Christ? Should I therefore take the members of Christ and make them members of a prostitute? Never! (1 Cor 6.15). The appeal to union with Christ is certainly a powerful one, and this kind of thinking can undoubtedly motivate a person to a purer life. Gregory of Nazianzus has a powerful passage somewhere in which he says that, in light of his union to Christ, so long as he does not obey God, he makes Christ to be disobedient and a sinner. It certainly has motivational power.
On the other hand, there are many things that I am within my rights to do, and yet I would not engage in them if I took this metaphor of union with Christ as real, as a metaphysical fact. It is within my rights to sleep with my wife, but I would not want to unite Christ's members to my wife any more than a prostitute. The counterexample is crude, I grant the point, but so was Paul's to begin with.
I will give another example. Steven Jeffrey, Andrew Sach, and Michael Ovey in Pierced for Our Transgressions (2007) argue that penal substitution and the doctrine of the imputation of righteousness are intelligible in light of the doctrine of union with Christ. Because Christ is really united to believers, their sins become his through this union, and consequently he can justly bear the punishment for them; on the other hand, because he is really united to believers, they really do receive his righteousness.
A realist interpretation of this doctrine likewise terminates in contradiction. If through union with Christ, I gain his righteousness and he gains my sinfulness, the logic of union dictates that what remains is a single person who is simultaneously righteous and sinful. This of course is a contradiction.
For reasons such as these, one might incline towards a nonrealist interpretation of theological statements such as these. They are useful descriptions and metaphors used in describing a reality that actually goes beyond the bounds of what we can know and understand. Salvation and its process is a mystery; theology is the way we attempt to describe what cannot be described, and understand what cannot be understood.
This doesn't mean that salvation is nothing at all. Believers know from their own experience that something is changed in them, and that they have real communion with the Father and the Son in the Holy Spirit. It is something real; it is just that its nature cannot be understood or named adequately. Neither does this mean that all theology is on a par. Paul's use of the metaphor of union with Christ in the context of consulting the services of prostitutes is extremely efficient, perhaps in a way that other metaphors or rebukes might not be. Moreover theology may still be inspired, even if not strictly speaking adequate in describing the metaphysical reality of things. Certainly it is possible that God wants us to theologize in a certain way (e.g., praying to him as Father) because it trains us to relate to him in a way that other theologies cannot do, and he gives us this theology in through the scriptures and the teachings of Christ. It may even be necessary that we firmly believe our theology as if it were a realist statement of the actual nature of things, because in this way it has the desired effect.
If someone complains that this would be tantamount to having a false belief and believing a lie, I respond that to the extent that we cannot know some reality in itself, we cannot have an obligation to believe rightly about it. On this view of the world there is no categorical imperative to have perfect knowledge, to believe only and all true things. But moreover if we cannot but come into contact with this unknowable reality, we have to believe something or other about it, and especially so if it tells us what we ought to believe, what we ought to say, etc.