I could write you a detailed explanation but it requires some WP/PHP knowledges.
In short : the fact that it's working with the old version of WP Better Emails was actually a misbehaviour of my plugin.
It's also working fine because WP-CRM sets their emails as 'HTML' but don't use any HTML inside them... If they used full HTML templates (like Woocommerce for instance), my plugin would wrap the content with a template around their template and it would mess things up (=> last update fixes this).
You should send your request to the WP-CRM developpers, they should propose a "format" option for sending emails in HTML or plain text.