In my case, JabRef can connect to the Snap version of LibreOffice Writer, but only if the writer is executed via command line:
/snap/libreoffice/65/lib/libreoffice/program/soffice --writer --nologo &
libreoffice-java-common is still required, even though the required jar files ("unoil.jar", “jurt.jar”, “juh.jar”, and “ridl.jar”) were in /snap/libreoffice/65/lib/libreoffice/program/classes. So, setting the manual connection to this folder is useless. I had to do:
sudo apt install libreoffice-java-common