What causes circular saw to wander when cutting?
Three things can cause wandering (or what seems like wandering). The first is a misaligned table and/or fence. The cut isn't actually wandering, but it seems like it is visually because of how the table is tracking across the workpiece.

The second is the use of modern "thin kerf" blades for rip cuts. While they're fantastically fast for crosscuts, they tend to "oil can" while cutting with the grain, which can cause severe wandering, especially with hard or thick boards. You'll have to work harder to keep a straight line or switch to a more conventional blade, wherein the heavier blade disk is more stable.

The third is user error. Are you applying rotational force as you push the saw? Are you preventing drag on the blade from doing so? The drag from the blade is slightly offset from the saw handle, so there's an inherent tendency for rotation in that direction. 

I suggest a second-finger-trigger grip--use your second (middle) finger for the trigger, and place your first (index) finger along the front of the trigger guard. This gives you much better torsional control of the saw. 

I've used Makita circular saws exclusively since the 1990s. They're consistently precise and smooth. Unless your saw has sustained damage or is extremely worn, this is probably worth consideration.