Recently, the practice has extended beyond academia and taken the Web by storm. Some writers at Slate and Salon seemingly engineer their sentences so that the case at the beginning of a quote is never, ever in context, thus allowing them to use their [n]ew [t]oy.
Others seem to think the brackets are the new ellipses, to indicate that something came earlier but isn't being quoted. Any quote that does not begin with the first word the speaker uttered as an infant gets [T]he [T]reatment. Bizarrely, this happens even with spoken quotations, as though people spoke in big and little letters.
If you're writing or editing in a rigorously picky environment, go ahead and use those brackets. Otherwise, perhaps with the occasional exception, do not. If a case change leaves you feeling dirty, rewrite the sentence to put the quote in its correct case-specific context.