Sure pick ups and EQ etc. Can even out any differences as said, but I am in the camp that not just the body wood, but fretboard wood make a difference in the sound that comes out - it has to.
Electronics for the most are not that variable as they are not living structures. If you straight lifted electronics from one bass to another, to another etc. There will be a variance in sound - you hear of people talking about dead, dull, lifeless basses.......
That being said I am not an exotic or any wood snob - I still agree with pick up and use the one that works for you whatever the make up and combination of woods, or non wood materials.