Hah, my parents were unsure before I started but now they're really proud and love telling everyone. They'll come round.
The other way to look at it is this - not all jobs actually require something specific. Sure, if you're going to be a doctor you'll need a medical degree, but many, many career paths just need a degree of any kind. Most of those who'll ask why you're doing Japanese or Chinese would approve of people doing History or English, degrees which are focused on the skills you gain rather than anything specific. Japanese and Chinese actually have more skills than those degrees though, people just don't realise it. You write essays, you have to be creative, you have to learn communication skills through seminars and group presentations, then you have an entire year abroad in a foreign culture on your own developing personally and doing all of the above all over again, along with, in Japanese at least, the year abroad project which builds writing, creative and research skills amongst other things. And that's all just the tip of the iceberg, you'll have tons to make potential employers interested in you. Plus there are language related jobs anyway - translation, interpretation, etc, if you wanted to go down that road. You'll be much more interesting than yet another History, English or Media Studies graduate.
Background? They don't hugely mind or matter. I only had a GCSE A in French and Latin with a year of Spanish in school and I was accepted and am doing just fine. If you were doing French and had done Spanish that would help, and Japanese would help Chinese as well as the reverse, but European languages don't really help Asian ones. Put in the work and you'll be fine.