Let logged-in users use radio buttons (yes and no) to exclude their author profile from the user listing

I’d add a meta key and value to each user first and then add meta_key and meta_value to the get_users argument array.

Your meta key could for example be called showme and value would be "yes". So wherever an author has a meta value of "no", get_users() would exclude that author.

Add this code to your functions.php:

<?php // you might not need this line when pasting into functions.php
add_action( 'show_user_profile', 'so_show_extra_radios' );
add_action( 'edit_user_profile', 'so_show_extra_radios' );

function so_show_extra_radios( $user ) { ?>
    <table class="form-table">
        <tr>
            <th>
                <label for="showme">Show profile</label>
            </th>
            <td>
                <input type="radio" name="showme" value="yes" <?php 
                    if (esc_attr(get_the_author_meta('showme', $user->ID)) == "yes")
                        echo "checked";
                ?>></input> Yes<br>
                <input type="radio" name="showme" value="no" <?php 
                    if (esc_attr(get_the_author_meta('showme', $user->ID)) == "no")
                        echo "checked";
                ?>></input>
            </td>
        </tr>
    </table>
<?php }

add_action( 'personal_options_update', 'so_save_profile' );
add_action( 'edit_user_profile_update', 'so_save_profile' );

function so_save_profile( $user_id ) {
    if ( !current_user_can( 'edit_user', $user_id ) ) return false;

    if (wp_kses_post( $_POST['showme'] ) == 'yes')
        update_usermeta( absint( $user_id ), 'showme', "yes" );
    else
        update_usermeta( absint( $user_id ), 'showme', "no" );
}

Then add your meta_key and meta_value arguments in your author.php (or wherever you retrieve your author profiles) as described here.