Yes. What defines the protocol is the endpoints, not the cable. Just avoid the "USB 2.0" USB-C cables, which do not connect all the pins (only the ones needed for USB 2.0). Of course, higher speeds and higher charging currents need a higher grade of cable, but that higher-quality cable will work with lower speeds and lower currents. Take a look at the Wikipedia article: https://en.wikipedia.org/wiki/USB-C

AIUI: nothing is protocol-incompatible, but Thunderbolt-compatible cables are short, stiff, and expensive. So you can buy only those, but you do make sacrifices to do so.