Partial solution using many classes

partial-solution-2.jsx

//(contents of the React component, simplified)
render() { // render method of component
// ...
// count the number of truthy booleans
const numberOfButtons = [canAddColumns, canHideColumns, canRemoveColumns, canSearch, canSort].reduce(
        (acc, showButton) => showButton ? acc+1 : acc,
        0
    )
<div className={
    classNames(
        {"column-icons-1": numberOfButtons === 1},
        {"column-icons-2": numberOfButtons === 2},
        {"column-icons-3": numberOfButtons === 3}, 
        {"column-icons-4": numberOfButtons === 4}, 
        {"column-icons-5": numberOfButtons === 5}, 
    )
}>
    { canHideColumns && renderHideColumnsTrigger() }
    { canSort && renderSortingIndicator() }
    { canSearch && renderSearchTrigger() }
    { canRemoveColumns && <RemoveColumnButton /> }
    { canAddColumns && <AddColumnButton }
</div>
// ...
}