With a real USB-C host, this is not just for orientation (which usually doesn't matter if you strictly use the D+/D- pairs, which are themselves supposed to be paralleled on your device in 99.99% of the cases), but primarily to make the host detect your device as a USB device. Otherwise, it won't even care to enumerate it. In theory, you could do with using only one of them on either CC1 or CC2, except that "standard" USB-C to USB-C cables only have one wire for CC (which is precisely made to enable orientation detection, when it matters), so that if you put only one of these resistors in your device on either CCx, it will only work in one orientation as the host won't see the device as a device in the other orientation.
So omit those two resistors, and your device won't work when connected to a real USB-C port. And omit one of them, and cables will work only in one orientation: nice way to irritate your customers! That may not be widely available on typical desktop computers yet, but most laptops do now and some don't even have USB-A ports anymore. So you really don't want to play with that. It won't feel nice.