This paper addresses the robustness of the constant-delay predictor feedback in the case of distinct and uncertain time-varying input delays. Specifically, we consider the case of a predictor feedback that is designed based on the knowledge of the nominal value of the time-varying delay in each control input channel. We derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the distinct time-varying input delays around their nominal value. Then we apply these results to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems exhibiting distinct time-varying delays in the boundary control inputs.