It's too early to expect real-world applications of anti-realism. Instead I would redirect your attention to a similar pattern in the foundations of mathematics.
Mathematical foundations were once very shaky, but real-world mathematicians didn't care in practice. Bertrand Russell showed that an early mathematical foundation attempt was inconsistent. At the time, to a working mathematician, this would have been about as airy-fairy as anti-realism seems to us today. A mathematician back then could well and rightly have said: "Proofs, equations, solutions, these are valuable things. But Russell's paradox? I challenge anyone to tell me something useful that has come from the study of Russell's paradox." Indeed, the paradox was actually known to Zermelo before Russell, and Zermelo didn't consider it important enough to make a fuss about!
Now in hindsight, we know that foundational work DID pay off in practical ways. It was a crucial step toward the development of, for example, automated proof verification software like COQ, which has extremely important real-world applications and whose importance will only grow in the future.
Here's my speculation: things like anti-realism are equivalent to Russell's Paradoxes which seem like navel-gazing today. In a hundred years' time, they might have proven to be a crucial step toward formal science verification software. Just like fixing mathematical foundations was a crucial step toward formal mathematical verification software.