To summarize, you are making a device that uses Type-C port to charge some inside battery when connected to a Type-C laptop, and also want to use the Type-C Rx/Tx pins as UART interface to some internal IC from some debug adapter. Your concern is whether your device can suffer a damage if someone plugs your device into regular Type-C laptop port (with regular C-C cable).
Your concern is not founded. The voltage level on Rx pins will occur only during "Rx detect" stage, where a common-mode pulse will be applied with 400 mV amplitude, making the voltage at 800 mV at best, and only for 10-20 ms. However, the voltage will have a negative peak as well, but your UART will likely tolerate this.
You can use the Rx/Tx wires as you wish, however you need to keep in mind that the Rx+/Rx- (and Tx) are typically twisted in pairs, so you might incur substantial cross-talk if you don't use the wires correctly. You need to use, say Rx- and Tx- as signal ground wires, and Rx+ and Tx+ as your UART signals.
More, to get any voltage from your laptop, you need to have 5.1k pull downs on each of CC1 and CC2 wires, otherwise the Type-C port will output no VBUS.
Also please be aware that USB Type-C specifications also "went an extra mile" and do define DAM - Debug Accessory Mode, precisely for the purpose of extensive debugging. The attach/discovery protocol is crazy IMO, but you might want to take a look at appendix B of the specs if you are serious. The transport layer is not defined, so you can use the simple propriety UART functions.