Quantifying the effects of textual interventions in social systems, such as reducing anger in social media posts to see its impact on engagement, is challenging. Real-world interventions are often infeasible, necessitating reliance on observational data. Traditional causal inference methods, typically designed for binary or discrete treatments, are inadequate for handling the complex, high-dimensional textual data. This paper addresses these challenges by proposing CausalDANN, a novel approach to estimate causal effects using text transformations facilitated by large language models (LLMs). Unlike existing methods, our approach accommodates arbitrary textual interventions and leverages text-level classifiers with domain adaptation ability to produce robust effect estimates against domain shifts, even when only the control group is observed. This flexibility in handling various text interventions is a key advancement in causal estimation for textual data, offering opportunities to better understand human behaviors and develop effective interventions within social systems.