Update: It seems the issue is related to aliasing (?). I've been playing Apex with no anti-aliasing since Season 1 and never encountered any problems.
After removing the config folder at [C:\Users\"username"\Documents\Respawn], the ironsight bug disappeared, so I wonder why. Then I tried to mess around with the video settings in-game.
When I turned off TSAA, the problem returned.
Now I have to enable TSAA (which is frustrating since it makes enemies appear blurrier, a setting I never use) to prevent the dot on the ironsight from spreading randomly while firing. This is just a temporary solution tho.
