Some more details:
Although the source pulls up both CC1 and CC2, the sink will only see either CC1 or CC2 become high (>0.20V) depending on the orientation of the plug, while the other CC-pin is not-connected or pulled down by the cable. More generally, whichever CC pin has the higher voltage during attachment becomes known simply as “CC”, which is also the pin used for Power Delivery (PD) communication. Brief (<10ms) low pulses on CC should therefore be ignored to ensure you don’t get confused if the source attempts to perform PD communication.
There is an obscure case where a sink will see both CC1 and CC2 high, which is when it is attached as target system to a debug/test system (DTS). Since this “debug accessory mode” of USB-C is inherently device-specific it’s already up to the end-user to avoid connecting an incompatible device to a DTS so you can probably just ignore this case, but ideally you should either consider yourself not-connected in this situation (and draw no power) or abide by the current limits shown below.
The following matrix shows all the info you can get from the CC pins as a sink device:
