Conventional domain adaptation algorithms aim to achieve better generalization by aligning only the task-discriminative causal factors between a source and target domain. However, we find that retaining the spurious correlation between causal and non-causal factors plays a vital role in bridging the domain gap and improving target adaptation. Therefore, we propose to build a framework that disentangles and supports causal factor alignment by aligning the non-causal factors first. We also investigate and find that the strong shape bias of vision transformers, coupled with its multi-head attention, make it a suitable architecture for realizing our proposed disentanglement. Hence, we propose to build a Causality-enforcing Source-Free Transformer framework (C-SFTrans) to achieve disentanglement via a novel two-stage alignment approach: a) non-causal factor alignment: non-causal factors are aligned using a style classification task which leads to an overall global alignment, b) task-discriminative causal factor alignment: causal factors are aligned via target adaptation. We are the first to investigate the role of vision transformers (ViTs) in a privacy-preserving source-free setting. Our approach achieves state-of-the-art results in several DA benchmarks.