Even though Culler writes that theory is roughly the theory of "signifying practices" or of "something like culture in the broadest sense", theory cannot be reduced to "the study of the background (...) that we bring to the text".
This is clearly not the case with a number of older theories he describes in the book's appendix on theoretical schools and movements (pages 123-132 in the first edition).
For example, Russian Formalism studied poetic language not so much to uncover a text's meaning but to learn about the mechanisms that constitute literariness.
New Criticism in the USA and werkimmanente Interpretation in post-war Germany focused on the work as such, isolating it from its cultural and historical context. (German professors of literature who had been involved with Nazism had "good reasons" to do this, i.e. avoiding drawing attention to their recent past.)
However, Culler's comment is mostly about the sort of theory that is not primarily about literature and draws on ideas from psychological, political and philosophical texts. But even the theories that have emerged since the 1950s cannot all be said to study the cultural or other background that readers bring to the text. Structuralism, for example, focuses on binary oppositions and other patterns in literary texts, i.e. patterns that vary in scope from the sentence level to the narrative as a whole and even intertextual connections. Post-structuralism in a sense "reads the text against itself", i.e. it reads a text as saying something quite different from what it appears to be saying on the surface (see Barry p. 74-75).
However, there are a number of reader-oriented approaches to literature, such as Hans Robert Jauss's aesthetics of reception (Rezeptionsästhetik) and reader-response criticism in general. There are also a number of theories that focus on forces and patterns that are at work in society or in people's minds (or both) and how these forces and patterns can be retrieved in literary texts. These theories include feminism, Marxism, psychoanalysis and post-colonial theory. Even though the "forces" I mentioned can be said to be at work in both readers and authors, the focus of such criticism tends to be directed at the text rather than either the reader or the author.
Much of the above needs to be qualified by the observation that criticism often doesn't rely on a single theory but combines concepts from two or more; for example, feminist criticism may draw on concepts from structuralism, psychoanalysis and Marxism (see the Introduction to Wolfreys & Baker). In addition, theory is never "finished", let alone as pure or straightforward as summaries in introductory works may suggest, so a specific type of criticms can always draw in concepts from theories that focus on cultural or other aspects when the need arises.
What we bring to the text may play a role in the background. In Russian Formalism, for example, a text's literariness would be hard to define without knowing the conventions of ordinary language from which the literary text deviates. But most theories in Culler's appendix don't seem to fit the description that they study "background (cultural background and/or other background) that we bring to the text".
- Barry, Peter: Beginning Theory. Fourth edition. Manchester University Press, 2017.
- Culler, Jonathan: Literary Theory: A Very Short Introduction. Oxford University Press, 1997.
- Wolfreys, Julian; Baker, William (editors): Literary Theories: A Case Study in Critical Performance. Macmillan, 1996.