Q. is it permissible to wear leather insoles or leather heel lifts in one’s sneakers on Yom Kipper?

A. Many Poskim maintain that even if a small amount of leather is part of a shoe, it becomes prohibited, They maintain that “shoes” refer to footwear that includes leather, even in a small amount. Accordingly, footwear made only of cloth (e.g., sneakers) or any other material, may be worn on Yom Kippur. See Shulchan Aruch, O. H. 554:16 and 614:2 following the Riff, Rosh, and Tur.
Rabbi Ovadiah Yosef (Yalkut Yosef, Moadim 5748] p. 90) permits wooden clogs with a leather strap.
Horav Shlomo Miller’s Shlit’a opinion is that one should avoid shoes that contain even small amounts of leather. In case of need, comfortable or well padded slippers or non-leather moccasins should be used, instead of leather insoles.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a