Darcie: Textile is an alternative system of encoding that some people prefer to HTML for its simplicity and ease of use. Ideally you can offer people a choice of either using Textile or HTML to encode blog entries, however, it seems that the two interfear with each other in the case of blockquotes.
I found a temporary fix, by reading this page. It seems that if the <blockquote> tags appeare after a space at the beginning of the line, Textile won't encode them. So, if you write your code like this, it will work:
[Damn, it is impossible to properly show the formatting of the code in these forums, even using backticks!]
Both the opening and closing tags need to be at the beginning of the line, with a space right before the code. I tested this on two systems and it works. Hopefully the makers of the Textile plugin will repair this bug, since one should really be able to use HTML encoding even if the Textile plugin is turned on.