rear tires shouldnt cause the pull that you are describing unless significant low air
I know that much that new tires in the front can cause some pull if your cambers are out a bit but the older tires rub in such a fashion that there is no pull
in your case its simply the older tires probably causing it which you happened to notice now, check your tires for inner and outer edge wear and you will find the answer(i think left tire inner edge)
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