Should a breadcrumbs navigation have links set to rel="nofollow"?
I think it depends what your goal is and what the breadcrumbs represent. I would say that for most wordpress sites nofollow on breadcrumbs is probably a nonissue.
Let's start with nofollow. Nofollow says you don't want a search engine to pass on page rank to this link. So if you had comment links and people can post their personal website you would probably use nofollow. This makes spamming your website link pointless because the links aren't being followed anyways.
Nofollow is also important because page rank flows evenly between links on the page. So if you have three links that are really important to you and then a hundred comments with random websites in them, you don't want page rank getting split 103 ways.
Now your question. If the breadcrumb items are important for search engines then have them followed. If you don't care about your breadcrumbs getting indexed then nofollow them. If it were me I would probably have my root node followed, the front page of my blog, and I would not have child nodes followed because those are just categories.