Current Sailfish OS versions enforce sailjail/firejail rules.
When one tries to export the list of podcasts into an OPML file, gpodder asks for a filename (i.e. does not present a folder selection screen).
The file is then saved into the user's home directory with a ".opml" extension.
However, the exported file never reaches the actual home directory but stays in the sailjail/firejail container and is lost when gpodder is closed.
As far as I understand the issue, gpodder would either

• a) need a SailJail profile with an explicit permission to access the home directory or (preferrable)
• b) need to export to one of the directories listed in /etc/sailjail/permissions/UserDirs.permission (e.g., Documents, Downloads, or Music) or to the SD card

Workaround: enter Documents/export.opml in the file name field when exporting the podcasts.

Alternative workaround (tried this first before looking into permissions; adjust the path to only get the .opml file you want):

PID=$(firejail --list | grep gpodder | cut -d: -f 1 )
firejail --cat=$PID /home/*/*.opml > /tmp/podcasts.opml