I honestly cannot comment on China, Cambodia, Cuba, or Vietnam
Mmmm...I can comment on Cuba. And as far as I know, it was never abolished. However, Christmas wasn't officially celebrated until 1998. Officially celebrated dosen't mean it couldn't be celebrated privately, it just meant the goverment didn't consider it a special day.

As for Cuba, well, when I was there I saw churches, I saw people praying, I saw crucifixes inside some houses, etc.

And as for those countries, hardly could you consider those people "liberal". They were absolute authoritarians. Left in economical policies, but politically authoritarian. The less authoritarian of the list may be Cuba, and it still has several rigid laws and death penalty. The liberal left would never abolish Christianity. The most far thewy could go is to reduce the public money the church recives.