Service rifle matches shoot ARs at 200, 300, and 600 yards with open sights. Most folks use 69-80 grain bullets at 600.
They're also shot at 1000 but that's pretty much the edge of the envelope IMO. For an AR you're talking 80 and up grain VLD bullets singly loaded because they're too long to fit in the magazine. And rifling 1:8 or shorter to stabilize the heavy projectiles. And maybe a throated match barrel. And, and, and..... Point is, it can be (and IS) done, but it is a non-trivial exercise. And you won't do it with run of the mill equipment and ammo.