Deformable multi-contrast image registration is a challenging yet crucial task due to the complex, non-linear intensity relationships across different imaging contrasts. Conventional registration methods typically rely on iterative optimization of the deformation field, which is time-consuming. Although recent learning-based approaches enable fast and accurate registration during inference, their generalizability remains limited to the specific contrasts observed during training. In this work, we propose an adaptive conditional contrast-agnostic deformable image registration framework (AC-CAR) based on a random convolution-based contrast augmentation scheme. AC-CAR can generalize to arbitrary imaging contrasts without observing them during training. To encourage contrast-invariant feature learning, we propose an adaptive conditional feature modulator (ACFM) that adaptively modulates the features and the contrast-invariant latent regularization to enforce the consistency of the learned feature across different imaging contrasts. Additionally, we enable our framework to provide contrast-agnostic registration uncertainty by integrating a variance network that leverages the contrast-agnostic registration encoder to improve the trustworthiness and reliability of AC-CAR. Experimental results demonstrate that AC-CAR outperforms baseline methods in registration accuracy and exhibits superior generalization to unseen imaging contrasts. Code is available at https://github.com/Yinsong0510/AC-CAR.