Is it possible to be both an anti-representationalist and a theist? Yes.
To refresh your memory (and mine) an anti-representationalist is someone who believes that it is inappropriate to measure the truth or correctness of a belief on the basis whether or not the picture of the world created by the belief accurately represents reality (what is “out there”). This extends to all beliefs whether they be religious, scientific, poetic, political, etc. For the anti-representationalist beliefs are not about painting the ‘correct’ picture of reality rather they are about creating habits of action which allow one to interact with the world in a ‘useful’ way.
Let’s examine the question: “Does God exist?”. To the anti-representationalist whether or not one says “yes” or “no” will depend on whether or not by saying “yes” the individual will be able to form habits of action which benefit him or her in some way. Someone would then answer “no” if the individual would not form beneficial habits of action. This has nothing to do with whether or not there is some person or otherwise that the term ‘God’ refers to in the world (or outside of it). Another analogy would be that of the “electron”. For the anti-representationalist to say that “an electron exists” or “that is an electron” is true just insomuch as belief in electrons allows one to form habits of action which allow one and one’s community to live more successfully (for instance, build computers). To ask a question as to whether or not it actually exists in the world apart from our experience of it and our habits is par for the course.
Paul Tillich, the mid-twentieth century theologian, in The Courage to Be states that to ever ask the question of whether or not God exists is inappropriate. This is because, according to Tillich, God is “that which all being [(existence)] flows from”. Tillich believes that since God is the source of all existence there is no proper way to talk of God as existing or not. Tillich believes that God transcends these types of questions. In this limited sense I believe Tillich may be called an anti-representationalist. Although, for the anti-representationalist this kind of “inappropriateness” extends to all objects (e.g. trees, other people, stars, the Moon, dirt, tables, chairs).
Because of people’s qualms about using language as though it strongly refers to objects in the world Tillich was often characterized as an atheist because he could not say that God exists. This, given the exposition above, is obviously not the case.
Anti-representationalism may strike many people as downright crazy: “What do you mean when I talk about chairs and tables I am actually not talking about them!”. A simple question to ask in response to this objection is whether or not you would act differently if I provided a ‘knock-down argument’ as to the truth that actually chairs and tables never existed and never will exist? If you would not act differently in light of this, this is a passive affirmation of the truth of anti-representationalism. Namely, you will still act as if they existed not because they really do but because you have very successful habits of action formed by the employment of the concepts of ‘chair’ and ‘table’.
If I am right there is no problem with being an anti-representationalist and living a strongly theologically based life.
Suggested further reading:
The Courage to Be, Paul Tillich
Philosophy as Cutural Politics, Philosophical Papers vol. 4: Ch 1 The Cutural Politics and the Question of the Existence of God, Richard Rorty