Redirect exclusion rule in .htaccess does not work
You're right, there's interference with other Drupal rewrite rules. If you have clean URLs enabled, you're rewriting each request as an argument to index.php. Add an additional check to exclude this other rule.

RewriteCond %{HTTPS} off
RewriteCond %{REQUEST_URI} !^/my_url
RewriteCond %{REQUEST_URI} !index.php
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]