Attention-based arbitrary style transfer methods, including CNN-based, Transformer-based, and Diffusion-based, have flourished and produced high-quality stylized images. However, they perform poorly on the content and style images with the same semantics, i.e., the style of the corresponding semantic region of the generated stylized image is inconsistent with that of the style image. We argue that the root cause lies in their failure to consider the relationship between local regions and semantic regions. To address this issue, we propose a plug-and-play semantic continuous-sparse attention, dubbed SCSA, for arbitrary semantic style transfer—each query point considers certain key points in the corresponding semantic region. Specifically, semantic continuous attention ensures each query point fully attends to all the continuous key points in the same semantic region that reflect the overall style characteristics of that region; Semantic sparse attention allows each query point to focus on the most similar sparse key point in the same semantic region that exhibits the specific stylistic texture of that region. By combining the two modules, the resulting SCSA aligns the overall style of the corresponding semantic regions while transferring the vivid textures of these regions. Qualitative and quantitative results demonstrate that SCSA enables attention-based arbitrary style transfer methods to produce high-quality semantic stylized images. The code can be found in https://github.com/scn-00/SCSA.