Says the Mishnah, Kilayim 9:3:
מִטְפְּחוֹת הַיָּדַיִם, מִטְפְּחוֹת הַסְּפָרִים, מִטְפְּחוֹת הַסַּפָּג, אֵין בָּהֶם מִשּׁוּם כִּלְאָיִם. רַבִּי אֶלְעָזָר אוֹסֵר.
Hand towels, covers for Sifrei Torah, and bath towels are not subject to the laws of Shaatnez. R’ Elazar forbids [using these made of Shaatnez].
Translation follows Bartenura.
According to the Tanna Kamma, why would I think that a Sefer Torah can’t “wear” Shaatnez? Is a Sefer Torah a person that it should be obligated in mitzvos? By the same token, why does R’ Elazar forbid them?