I found out the WP_Customize_Manager class has a function called remove_section(). In your function hooked to customize_register you can just do:
$wp_customize->remove_section('nav'); $wp_customize->remove_section('static_front_page'); You can find the ID of the section (i.e. 'nav') if you inspect the accordion title bar of the section. Look at the ID of the containing <li> tag and it's the portion of the string after "customize-section-". I.E.:
<li id="customize-section-static_front_page" class="control-section customize-section"> -- the ID is "title_tagline""static_front_page"