Fusion-based hyperspectral image (HSI) super-resolution has become increasingly prevalent for its capability to integrate high-frequency spatial information from the paired high-resolution (HR) RGB reference image. However, most of the existing methods either heavily rely on the accurate alignment between low-resolution (LR) HSIs and RGB images, or can only deal with simulated unaligned RGB images generated by rigid geometric transformations, which weakens their effectiveness for real scenes. In this paper, we explore the fusion-based HSI super-resolution with real RGB reference images that have both rigid and non-rigid misalignments. To properly address the limitations of existing methods for unaligned reference images, we propose an HSI fusion network with heterogenous feature extractions, multi-stage feature alignments, and attentive feature fusion. Specifically, our network first transforms the input HSI and RGB images into two sets of multi-scale features with an HSI encoder and an RGB encoder, respectively. The features of RGB reference images are then processed by a multi-stage alignment module to explicitly align the features of RGB reference with the LR HSI. Finally, the aligned features of RGB reference are further adjusted by an adaptive attention module to focus more on discriminative regions before sending them to the fusion decoder to generate the reconstructed HR HSI. Additionally, we collect a real-world HSI fusion dataset, consisting of paired HSI and unaligned RGB reference, to support the evaluation of the proposed model for real scenes. Extensive experiments are conducted on both simulated and our real-world datasets, and it shows that our method obtains a clear improvement over existing single-image and fusion-based super-resolution methods on quantitative assessment as well as visual comparison.