You have to inline the css into your theme. CSS is read-only and can’t updated to use the update hex colors for your header.
<?php echo get_theme_mod( 'header_textcolor' );?> 100%);">
So find the div in your theme called navbar-default and update it to this:
<div style="background:#<?php echo get_theme_mod( 'header_textcolor' );?>"> class="navbar-default">