I'm using a Play-Store-less microG LineageOS on a Google Pixel 1, and all my banking apps work (Revolut UK, German Post Bank authenticator), as well as a Swiss online health care app.
I haven't found an application yet that I couldn't use on LineageOS due to lack of SafetyNet.
Regardless, Google already has enough information on me to profile me quite well; avoiding Google Pay will not meaningfully change that, and I get enough value out of it that the trade off is worth it to me, at least for now.
However, for people who want to use Google Pay despite the privacy implications, I'm not sure running a privacy-preserving Android distribution is even meaningful. At that point, why not just run stock Google Android?
Isn't that like 99% of their revenue i.e selling user data?!