It turned out that the issue was caused by unrar converting the filenames into UTF-8 when extracting the archives, so the special Windows 1252 characters (e.g. Ø) were replaced by their UTF-8 equivalents. This is the default behavior of all utilities capable of extracting rar files, and it's entirely sensible considering that UTF-8 is the standard on Linux and so non-Unicode characters in filenames, although possible, look like gibberish. However, because of this the IA installer complained of not being able to find the extracted files, and when I forced it to do its job anyway, it used the wrongly (from BG2's perspective) encoded filenames and this caused the game to crash.
The solution was to force unrar to preserve the original Windows 1252 (equivalent to ISO-8859-1) encoding, which I was eventually able to achieve by setting the right locale via the LANG environment variable, e.g.:
LANG=en_US.ISO-8859-1 unrar e "$MODS_DIR/IA_Fiends_Genies.rar" "$BG2_DIR/infinityanimations/content"
With this, the IA installer was able to find the archives and install all components successfully, and the game crash was also gone.
I am quite sure anyone attempting to install IA on Linux will encounter this issue, and the solution is very unobvious from my perspective. Maybe it's a good idea to add a sentence to either the Linux or the Troubleshooting parts of the Readme, perhaps with a link to this thread?