Is it true that using brushes (rather than fingers or sponges) to apply makeup products reduces wrinkles - as the result of causing less pulling and tugging on the skin?

Skin wrinkles due to three main causes. The first cause is genetics/aging. The second is UV exposure and resulting skin damage. And the third is movement of the skin, like facial expressions, or over manipulation of the skin from external sources. This repeated movement of the skin can eventually cause the collagen layers to be less elastic and can result in wrinkles.  I  think that the first two factors trump the third in terms of causing wrinkles. So, although there may be a slight difference in how much the skin is pulled from fingers vs. brushes, I would not worry about either.