Not necessarily, I have quite a few that work.

It's crowdsourced and therefore incomplete but https://plexus.techlore.tech/ has reports of compatability with the complete absence of Google Services or a replacement like MicroG.

Here in Switzerland my experience is that the big banks like UBS and the cantonal banks tend to work, while the smaller things like McDonald's and my credit card providers tend to break because they have nonsense Play Integrity requirements.