Works with caveats

MMR doesn’t support @include as its a Sass thing. Minification with a htpasswd protected site should work however. It might take longer to do the minification but I see no reason why it wouldn’t work.

I think the minification runs at a later time. That means that the credentials seems to become lost and the cron job cannot login to the site. One can just temporarily remove protection offcourse.

@include should be standard CSS as far as I understand. However ticking the flag in options seems to do noting so I hardhacked the code to skip minification of CSS so that works.

Hope my reply is useful for further dev.

Minification is performed on a wp-cron which is created by a page load, or on a schedule as a backup. It is possible wp-cron is not firing. Are you able to check that it is working?

Do you mean @import? @import is standard CSS, whereas @include is a Sass thing. MMR will not merge files that have @import. This is to ensure compatibility. If you know that your CSS doesn’t have any @import statements then you can skip checking for extra speed.

Yes, you are right sorry for the confusion. I have a :
@import './coloursonly.css';
statement
However at my side the flag for skipping CSS does not work and minification of CSS with @import ‘./coloursonly.css’; does not work.

Im not sure about the cron but it does not minify if the folder is .htpasswd protected

Do you have any errors in the logs?
Also, if you can change the @import to a wp_enqueue then I believe you will get a better result.