Even if you insist on having closed-source apps from the Play Store on your device you don't need to install the actual Play Store or any of its dependencies. Use either Yalp [1] (or its derivative Aurora [2] for those who want a more polished interface) and you can install free Play Store apps without ever needing to sign in to Google.

[1] https://f-droid.org/en/packages/com.github.yeriomin.yalpstor...

[2] https://f-droid.org/en/packages/com.dragons.aurora/