Learn Italian: Qualunque taglia va bene.

No, in this context they mean exactly the same thing ("any"). You could just as easily say Qualsiasi taglia va bene. Both words are invariable, meaning they do not change their endings to match the gender or number of the noun they describe.

Would the meaning change if I put qualunque after the noun, like Una taglia qualunque va bene?

Yes, slightly! When qualunque (or qualsiasi) is placed before the noun, it simply means "any" (no matter which one). If you place it after the noun, it takes on a slightly negative or dismissive tone, meaning "ordinary" or "mediocre." Because we just mean "any size will do" here, it goes before the noun.

Why use taglia for "size" instead of misura or dimensione?

Taglia specifically refers to standard clothing sizes (like S, M, L). If you were talking about shoe sizes or exact physical measurements, you would use misura. Dimensione is used for the physical proportions or scale of an object (like a box or a room).

Why does the sentence use va bene ("goes well") instead of a direct translation of "is fine"?