Personally I block all third party fonts and have never noticed an issue with a plain old font. The web is so much nicer with a very restricted font set and range of sizes.
Only thing I've noticed breaking badly are symbol fonts that try to be clever with ligatures, so that e.g. "arrow_right" gets turned into an arrow symbol. Happens a bunch on Google documentation sites.
As is pointed out in the article for the most part fonts are a form of progressive enhancement and lacking the font normally doesn't actually break a website. Unless a little less pretty == broken of course.
As someone who browses with "browser.display.use_document_fonts=0", virtually no site breaks without its fancypants fonts.