Standard quantum mechanics is usually taken to imply a very constrained type of anti realism, but not a broad general anti realism.
The type of anti realism it DOES NOT imply: there's no such thing as objective reality, there are no facts, human minds manifest the world by force of will.
The type of anti realism it CAN imply (but doesn't necessarily imply): properties we're used to thinking of as having concrete, singular values are in fact not as concrete or singular as we assume. In particular, the location and momentum of a particle at any given time: the naive view of the world is, at any given time these are facts about a particle, and if we don't know those facts that's just a matter of our own personal ignorance, not any sort of fact about the world.
Quantum mechanics suggests that, prior to measurement, some properties are not just unknown prior to measurement, instead those properties really don't and cannot have a concrete singular value. Bell Tests are the most important piece of evidence in this direction.
This "measurement" thing becomes a problem that leads people to think it means some kind of anti realist, woo, spiritual "our minds are creating the world" stuff, but that's not the case - or at least, not necessarily the case, that's not how most physicists think of it. Measurement has nothing in principle to do with human beings or minds.
But just because some values don't have concrete singular values prior to measurement doesn't mean there aren't any true facts about that particle. It's just that those true facts are a bit more strange than the naive view we're used to thinking about.