Obviously, this has nothing to do with my mail system. These are false positives where the receiving mail server finds something in my e-mails it does not like – but what? I had not attached anything and the messages were just a few lines of text.
As it turned out some security products do not like URLs in e-mails. In all cases my messages went through once I removed any links I had added. In cases where my messages did not contain any links I removed the URL to my website in the signature.