Q. And if so (that they were redeemed on the merit of not changing their clothing), how did the Jews leave Egypt wearing borrowed Egyptian clothing, that seems ironic?

A. Mefarshim address this question and they answer that the posuk (Shemos 3:22) states “Each woman shall borrow from her neighbor and from the dweller in her house silver and gold objects and garments, and you shall place them on your sons and on your daughters, and you shall empty out Egypt.” The fact that the text says; and you shall place them and not; they shall wear them, indicates that they only carried them as an adornment (Likutey Eish p. 85 quoting the Shinaver Rebbe, Siach Sholomo p.193.) Alternatively, that is why they used them only for their children, as they were of a smaller size and were therefore properly covered. Alternatively, they had them fixed and altered to fit them correctly (Levush Yosef p. 39 quoting Divrey Yechezkel.)

Horav Shlomo Miller Shlit”a explained that some particular garments, such as capes, mantles and shawls etc, were not exclusive used by the Egyptians, but were universally worn and were also of a modest design.

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