In 1926, H.W. Fowler offered a suggestion about making the English language a little tidier. In examining the various and inconsistent manifestations of the relative pronouns that, which, and who, he wrote that "perhaps the line of improvement lies in clearer differentiation between that & which."
That suggestion, in the first edition of Modern English Usage, has ossified into a Rule among American editors. In a post at Lingua Franca, "A Rule Which Will Live in Infamy," Geoffrey Pullum calls this "a quixotic reform effort" and a time-wasting fetish, and points out that there are several exceptions in which the restrictive which is perfectly appropriate in standard written English.*
Now at Sentence First, Stan Carey points out examples of nonrestrictive that, which the usage manuals used to label as rare but which appears to be on the rise.
I have noticed it myself. Over the past few years, I've come across a handful of non-restrictive thats nearly every week at The Sun, and I am puzzled at their appearance. For the moment, I can only offer a tentative surmise, that the that/which fetish has put it in the minds of uncertain writers that there is something tricky about which, so that is safer.
I have been swatting them rather than smothering them in the collection jar, so I have no examples to offer at the moment. If you have been seeing this phenomenon, I would be grateful for your observations.
Bonus link: Also at Lingua Franca, Professor Pullum discovers, perhaps not to his surprise, that the House of Lords includes "a bunch of grammatically ignorant sexist old fools." He is writing about singular they, with links to three previous posts at Lingua Franca on the subject. If you are still holding out against it, be advised: it is not going away.
*There is plenty of terminology, depending on where and when you learned grammar. I learned restrictive and non-restrictive clauses. You may have been taught essential and non-essential or limiting and non-limiting.
Linguists use defining or integrated relatives and non-defining or supplementary relatives.
For your purposes, just try to remember that if the clause can be taken out without changing the meaning of the sentence, it is parenthetical, non-restrictive, non-essential, non-limiting, non-defining, or supplementary. Put commas around it.