We investigated your problem and see that it is not theme-related. Because we tried to import XML files manually through the default “WordPress Importer” interface and still have the same problems.
But we found some workaround on wordpress support forum https://wordpress.org/support/topic/failure-to-import-and-invalid-post-type-errors
Here is the actual instruction
1) Download and Install 7zip.
2) Right click on your .XML file -> 7zip -> Add to Archive. You can find XML files in
3) Change the “Archive format” to gzip and hit “OK”
4) Try to import the file again (using the .gz you just created) and it should work. Admin panel -> Import -> WordPress