I need 1 1/4 cups of white rice flour for shortbread recipe, how much corn starch do I use as an alternative?
White rice flour is basically pure starch. You can generally substitute it 1:1 with other starches, and that functions in the vast majority of recipes without any noticeable difference in the finished product.
There is indeed some difference in starches from different sources, but since nonwheat flours are not normed anyway, there will be as much difference between white flours made from different cultivars of the same plant, or made by different producers (brands) than as between one source and the next.
This is not a substitution I would try, if the rice flour were the primary grain used in the recipe (that is, the majority of the flour).
White rice flour is not a pure starch. It contains some protein, non-dietary fiber, sugars, and minerals. This gives the rice flour body and structure and "bulk".
Whereas corn starch is almost a pure starch, with very little in it other than starch. This means that it "collapses" into a goo when mixes with water, and provides no structure at all to your baked goods. It's really only suitable for supplementing other flours, and certainly not as the major ingredient of shortbread. Even the classic Canada Cornstarch Shortbread contains twice as much wheat flour as corn starch.