It might help to put some numbers on how much parallax error a scope without an adjustable objective can introduce.
This simple equation predicts the apparent motion of the image at the target which is possible with maximum side to side eye movement:
FF= factory focus distance (typically 100 yards)
TD= target distance scope to target. Must be same units as FF
Obj= diameter of the scope's objective lens (must be the same units as Pmax.
Pmax = maximum parallax apparent movement. Same units as Obj
Pmax = Obj * (TD - FD)/FD
Example, if you have a scope with a 40mm objective with a factory set 100 yard fixed focus for zero parallax and you're shooting at 400 yards then if you move your eye laterally for the entire distance the target is visible though the scope the apparent movement of the reticle at the target will be:
Pmax= 40mm* (400-100)/100 = 40*3 = 120mm = 4.7 inches. The amount of possible error from where you wanted to aim (the center) would be half that or 2.4". Will you ever hold your eye so that it's right at the edge of the field of view? Probably not, so the actual error will be less than that. At 1000 yards those numbers would be 40mm*(1000-100/100 = 40mm*9 = 360mm = 14.2 Inches for having your eye mis-centered from edge to edge in the field of view. Half of that would be unacceptable for hunting big game. Notice that a larger objective allows further eye movement and thus more possible parallax error relative to the target.
Is an adjustable objective better? If you're last shot was at 25 yards and you forget to re-adjust the objective for a 400 yard shot you'll introduce nearly four times as much error as if you had a fixed 100 yard objective. If you set it for the correct distance with each shot at different distance parallax error will be eliminated. If you do have an adjustable objective I'd suggest leaving it set at a distance about 2/3 of the maximum distance you may shoot. Then if you forget to adjust it before a shot you can't introduce a parallax error larger than half the diameter of your objective at any distance and usually much less.
With any fixed focus scope you need to know it's factory objective focus setting. Many pistol scope are set to only 25 yards