The bug
The crosshair in the middle of the screen is off center by a few pixels. In my case the distance to the left side of the edge of the window is 1880 pixels, but on the right side the distance is 1888 pixels. This is especially obvious when the pause menu is open.
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migrated
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The reason this happens at all is just silly.
It's a 16x16 pixel texture* that gets put into the center of the screen.
But because the crosshair has an odd amount of pixels (9x9) it's impossible for it to be centered on the screen. More specifically the bottom right corner of the center pixel of the crosshair is exactly in the middle of the screen because that's where the center of the 16x16 texture is.
The eaiest fix would be to just change the crosshair design to have a 2x2 Center.
* They tried to fix it in the past by cutting off the bottom and right row of pixels to make it a 15x15 texture, but it didn't work at all as it's still centered like it's 16x16, just with some pixels missing on 2 sides.
EDIT: sorry for the overly large image i didn't expect it to be so massive. fixed by a mod
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Still in 1.16.3
It's completely doable. Evidence for this is the fact that the Crosshair when you have pressed F3 is centered.
[media][media]
Avoma
Can confirm in 21w11a.
Avoma
Can confirm in 21w15a.
Avoma
Can confirm in 1.17.
ampolive
Can confirm in 1.18 Pre-release 1.
Avoma
Can confirm in 1.18.1.
Avoma
Can confirm in 1.18.2.
Avoma
Can confirm in 1.19.
migrated
It looks like the crosshair is actually shifted either to the left or the right, depending of the size of the game window:
[media][media]There is also probably the same problem with top/bottom alignment when adjusting the window height, but this is more difficult to observe.
Added screenshot showing the issue from an official Mojang stream