Lovecraft was going through some pretty significant changes during the last decade of his life, both in terms of his writing and his politics. During the 1920s and early 1930s, he is typically seen as favorable (or at least amenable) to some form of fascism, and he cites it favorably in a handful of stories (most notably The Shadow Out of Time). But Lovecraft was also profoundly self-critical, and some of the letters he wrote shortly before his death suggest that he was in the process of revising his earlier viewpoints.
Lovecraft certainly had a powerful streak of racism, which emerged in his work both overtly (in works like The Horror at Red Hook) and metaphorically (I tend to give credence to the idea that The Shadow Over Innsmouth can be seen as a parable of the dangers of miscegenation). All that being said, however, I think there's a tendency to misread his racism as something atypical for the time. The same can be said for his sexism. Had he survived, I doubt he would have been a huge proponent of civil rights, but I don't think he would have taken a strongly negative stance, either.
As for the evolution of his writing style, I think it would have continued to progress from his early, essentially supernatural works towards a more sci-fi oriented approach. Science fiction had always been a strong current his work, even in early stories like Cool Air and Herbert West, Re-Animator, but I'd argue that it didn't become the dominant aspect of his material until the early 1930s, with stories like The Whisperer in Darkness, At the Mountains of Madness, and The Shadow Out of Time, where he started to reinterpret events of his earlier work through a much more overtly sci-fi lens.
I expect he would have continued along those lines, but I'm not sure how successful he would have been in finding an audience. A lot of his material from the 1930s had a hard time getting published in more science fiction-oriented magazines because he had been pigeonholed as a writer of "weird horror" earlier in his career. His tendency to disparage his own work meant that it wasn't until his legacy had fallen into the hands of people like August Derleth, who were more dogged in their approach, that a lot of his work saw print. That said, Lovecraft had oodles of connections amongst other pulp writers, so he'd probably keep at his craft. Assuming he lives through the 1940s, he'd undoubtedly find a wealth of material in the early atomic age to work with, and the explosion of sci-fi fiction in the late 1940s and 1950s would probably catapult his work to greater popularity.
Unless correspondents like Derleth convinced him beforehand, I expect that the first real collections of Lovecraft's work would start appear in the 1950s. Depending on his financial situation, I expect he would find some work in radio or television, but I can't imagine he particularly like it, given his temperament. A lot of his work would actually be quite well suited to early television. While some of his most famous, "epic" works would be hard to adapt given the budgets and technology of the mid-twentieth century (no "Call of Cthulhu" or "At the Mountains of Madness," to be sure), stories like "The Music of Erich Zann," "The Horror of Red Hook" (minus the overtly racist elements), and especially "The Colour Out of Space," all of which feature an essentially unseen threat, would adapt quite easily to the television format.
In general, though, I actually think Lovecraft's legacy would be lessened for his survival. He may well have produced a number of memorable works, but he lacked the promotional instincts of people like Derleth. His material would probably not have been packaged and organized as completely, and though he still would have had a huge impact on the development of "weird literature," I suspect he'd have even less name recognition among the public at large than he does today.