The update is kind, the solution does not work with React, however the addition below does.
onDragStart={(e) => { e.preventDefault() }}
EDIT: returning false for ondragstart no longer works for more modern versions of Firefox (credit: Hooman Askari), in this case use below.
function dragStart(e) { e.preventDefault() }
... and on the element
ondragstart="dragStart(e)"
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