Halakhah for Yoma 156:1

And concerning the shoe (sandal), our teachers - God should protect them - explained that a shoe is always of leather. And that is what is forbidden on Yom Kippur, but not of a different type. And the principle of the matter according to some commentators is that anything that is fitting for the matter of release (chalitsah) - meaning to say, that it is of leather - is forbidden on Yom Kippur, and permitted to go out into a public domain with them (wearing them) on Shabbat. But anything that is not fitting for release - such as cork and reeds and palms (see Yoma 78b, that it is a shoe of grasses) and other types of grasses (plants) - are permitted on Yom Kippur, so long as they do not go out with them [to a public domain] in a place without an eruv, as we consider them like a burden (and not a piece of clothing, which is permitted). But from the commentators, there are [also] many honored ones that permit one to go out into the public domain with all of them.