I am unable to use the mouse to interact with the 'Input Required' modal displayed when trying to run a build with parameters from the blue ocean UI.

This appears to be because the modal is mounted as a child of the branch row element, which is a link element. Clicking anywhere on the modal (inputs, buttons etc.) navigates to the page pointed at by that link (ie, the last run of that branch). I am only able to run parameterised builds from blue ocean by using the keyboard to navigate.