Mozilla acknowledged this issue and said that “Mozilla remains resolute in its commitment to privacy and user control. The new tab thumbnail feature within Firefox does not transmit nor store personal information outside the user’s direct control.” Mozilla promises that it will fix this issue in a “future release.”
Overall, the risk of somebody stealing your identity because of this seems pretty small, but the browser probably shouldn’t capture screenshots from pages that sit behind login pages and from secure sites. Just to be on the safe side – and especially if you are on a shared computer – it’s probably be best to turn this feature off for the time being. On a shared computer, of course, you can also use Firefox’s Private Browsing Mode (which you should probably do anyway if you are using a public machine).
Google’s Chrome and Opera have been using similar new tab pages to make accessing often used pages faster for quite a while now. There has been some limited discussion of the privacy implications of this feature in Chrome, but these two browsers use smaller and hence harder to read thumbnails than Firefox. Maybe that’s why we never heard much about these thumbnails as a security issue so far. Firefox, however, uses relatively large thumbnails to begin with and they also scale with the size of the browser window.