Auto sync with new computer will erase iphone contents those not purchased from itunes store.
itunes blocks this function since itunes is the tool with one way to transfer files from itune to iphone. you
must utilize other tools to achieve that. There're couple of tools for transferring the files between iphone
and computer (for backup)depends on your demands, e.g transfer only songs/videos, transfer photos etc. You can have a look of below review site, hope it useful.