I came across a small bug.
To recreate the bug
create a blank install
install Responsive theme and Polylang
add two languages
Then access the home page, the default language will show the custom homepage but the homepage for the second language will display a 404 error.
Solution - translate the Hello World! post or delete it permanently.
Cause - The reason is that themes with custom home pages have the reading settings set to latest posts but display their own content.
P.s. This problem should be solved for Responsive in version 1.9 but themes like Pitch still have this problem.