Why does Google Pinyin Input need to access my contacts?

Usually keyboard apps want to access your contacts for "predictive search" and auto-correction. If you don't like that, it should be fine to reject that request (and thus not giving them access) – without any "harm" to the app. Only it then won't know your contacts' names and cannot use them for auto-correction and "predictive search", of course.

That the request popped up while you were not even using the app might also be normal: depending on how it was programmed, it might want to update its dictionary while not being actively used. That it does so when you've never ever used it, is either bad programming or intentional bad habit (of course seen as a service to you, as it's always the case with pre-installed bloatware).

If this worries you, you can go to Settings › Apps, switch to the "All" tab (to show all apps, including the pre-installed ones), scroll to the app, tap its entry, and see if you can uninstall or at least disable it.