There are certain rumors that seem specifically designed to make the Internet explode. So specifically designed, in fact, that you find yourself not actually believing them, because of course casting directors wouldn't be so obvious. The rumor that Tom Hiddleston might join Sherlock Season 4 as the third Holmes brother is one of those rumors.
The third Holmes brother, it should be noted, does not actually exist within the Arthur Conan Doyle Holmes canon — he was invented by Holmes scholar William S. Baring-Gould in his Sherlock Holmes "biography," Sherlock Holmes of Baker Street: A Life of the World's First Consulting Detective. There was, however, a small shout-out to this hypothetical brother in BBC Sherlock's Season 3 finale, "His Last Vow," when Mycroft is talking to Sherlock:
I'm not given to outbursts of brotherly compassion. You know what happened to the other one.
Given the information, Sherrinford Holmes— again, not a canonical name, but rather one generally accepted by pockets of the vast, historical Holmes fandom — is probably not in the best of shape if he is indeed a part of this particular iteration of Holmes. In fact, he sounds kind of dead.
But what if he's not dead, and is indeed alive and destined to be played by British heartthrob Tom Hiddleston? Well, for one, Tumblr would have a fucking field day.
There are a few actors at work in terms of the believability of Hiddleston's alleged casting in Sherlock. One is that Sherlock has never been a show particularly interested in raking in guest stars or utilizing stunt casting — and considering the massive overlap in Hiddleston's fanbase and that of Sherlock, this could definitely fall into that category. In fact, Steven Moffat and Mark Gatiss have long seemed much more interested in nepotistic casting — Benedict Cumberbatch's parents, Martin Freeman's longtime partner, Mark Gatiss' partner, and Steven Moffat's son have all appeared in onscreen roles on the show. This could work in Hiddleston's favor, as he and Cumberbatch are friends (fun fact: Tumblr calls them Cuddles).
As for whether or not the third Holmes brother will appear at all in the show's fourth season (or at all), all Steven Moffat said when asked about the mysterious Holmes was "wait and see!" In Moffat language that could just as easily mean "we have literally nothing planned, for ever" as it could "he'll be a main character next season."
I'd say the biggest thing working against this casting, though, is that this news is coming from almost no outlet other than Christian Today. Before that there was only one report that I could find saying Hiddleston would be joining the cast of Sherlock — as "Sherrinford" or as anyone — and it was from this past April.
It's easy to imagine, in the incestuous world of British acting, that Hiddleston would join up with a heavily credentialed, breakout BBC show. And if it actually does happen, it will be undoubtedly glorious. But with things like this it's fitting to ask: "Is this the sort of thing that seems so perfect it's almost suspicious, as if someone made it up specifically to appeal to the tumblr audience?" As someone who spent much of the hiatus between seasons two and three fantasizing that they'd cast Hiddleston as Moran, I feel I have the authority to say that yes, this could easily be one of those times. I'll trust it when and if it's officially announced.