Lets put some numbers on it . Any non AO scope will be focused at some fixed distance. That distance is chosen by the manufacturer, but is typically 100 to 200 yards, maybe 50 yards for 22 and handgun scopes. How much error can it cause? if your eye is at the edge of the exit pupil the point of aim at the target can apparently shift by:
Dt Distance to the target from the scope.
Ds Distance from the scope to it's (factory or not) setting where the target image is focused on the reticle
Rs radius of the scope's objective lens
Rt radius of point of aim error at the target.
Rt = Rs *(Dt-Ds)/Ds
Note that Rt switches sign indicating which side of the target the error is located depending on whether Dt or Ds is larger.
Units. Ds and Dt must use the same units but it doesn't matter what units. Typically yards or meters.
Rs and Rt must use the same units but it doesn't mater what units. Typically inches or millimeters.
All are linear measurements, not angular measurements. (not mils or moa).
So if the scope focus distance is 100 yards and you have a 50mm objective scope (radius 25mm or approximately 1 inch) parallax error will be zero at 100 yards. For a target at 50 yards (or 150 yards) the maximum parallax error would be a half inch. At 200 yards it could be 1 inch, at 300 yards two inches. At 1000 yards it could be nine inches.
If the scope was focused at infinity instead of 100 yards the maximum parallax error at any distance would be only one inch, but it could have 1" of parallax error any distance.
It's unlikely that you would hold your eye right at the edge of the exit pupil, so the actual parallax error is likely to be half or less what the above equation indicates. This is not related to the quality of the scope or it's magnification. Scopes with larger diameter objective lenses can have proportionally more parallax error.
I use fixed focus scopes on rifles (mostly AR's) that I shoot offhand at up to a few hundred yards. On any rifle shot from bipod or bags I use adjustable objective scopes. An AO scope which is set incorrectly can introduce more parallax error than one with a fixed objective. I leave my AO scopes set to 2/3 the longest distance I'm likely to shoot that particular rifle. That's keeps the maximum parallax error to well under under an inch at any distance if I don't have time (or forget) to set it.