Well it turns out to be pretty simple to have it running, and don't have to risk having SIP disabled.
You have to turn off SIP to successfully install the extension, but when it's installed, it's enough to add an exception for kernel extensions from the ASIX manufacturer, so that you can turn SIP on again without breaking it.
reboot to recovery mode (CMD+R at boot) and open up the terminal
csrutil disable
reboot
install the latest version of the driver from asix: https://www.asix.com.tw/en/product/USBEthernet/Super-Speed_USB_Ethernet/AX88179
allow it in System Preferences -> Security & Privacy
reboot to recovery mode again and open up the terminal
csrutil enable
spctl kext-consent add 5RHFAZ9D4P
reboot