Is there some way around this?
Their software should just let them view the email without HTML in that case. They've chose to use email like that so leave it up to them. I have the same feature in Thunderbird and just toggle HTML on per-domain once trusted.
Is there some way to send auto emails in both HTML and TEXT format so that text only email software can also see the messages?
No, we don't have a way at this time to send multi-part emails (2 different content bodies). This will likely be supported once we support email templates. I'm unsure if Joomla email templates or mailer API supports this either though as we'll be switching to Joomla mailer API with CB 3.x (possibly in CB 2.7 as well).