We've never heard of that issue before and can't really see why that's happening. The code we use to insert that CSS file is the 'standard' Joomla way to do so. The specific line of code is in the /modules/mod_sclogin/helper.php file, at line 56:
$this->doc->addStyleSheet(JURI::base(true) . '/media/sourcecoast/css/common.css');
There's even another similar line at 65 which adds the theme stylesheet, which doesn't seem to be showing in the RSS feed. I can't understand why one would show and one wouldn't. When using the standard Joomla RSS feed, it automatically adds any stylesheets that have been added to the document.
One thing you could try is editing the helper.php file, and alter that line so it looks like:
if ($this->doc->getType() != "html")
return;
That should prevent our code from executing when an HTML page isn't being rendered.
Let us know how that goes,
Alex