In order to prevent WordPress from redirecting the subdirectory (and loading the 404 template), you must add a rule to the .htaccess file, BELOW the WordPress rewrite rules, with a line for each subdirectory, like so:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress
# BEGIN Subdirectories
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_URI} ^/subdirectoryname1/(.*)$ [OR]
RewriteCond %{REQUEST_URI} ^/subdirectoryname2/(.*)$ [OR]
RewriteRule ^.*$ - [L]
</IfModule>
# END Subdirectories