I am not an expert.
Many many apps rely on google play services to function, basically for most of the data fetching, push notifications, authentications, etc. Disabling it will break those apps as a result. Since your data is fed through those services you cannot maintain privacy from google without doing so.
So yes, you should disable google play for privacy, but you will need to find replacement apps in many cases.
Graphene does a thing where it "sandboxes" google play services, preventing it from grabbing unnecessary data like your real time location telemetry. I think this lets you use those apps that need it, but they will still get some of your data where thats being used. Banking apps are notorious for needing it for authentication, but you can easily use a different map app like magic earth to avoid google services for other needs.
I'm still exploring this and learning so those are just examples I know of. Not sure how much else this will break if you aren't using graphene to manage it.
I am wary of ever recommending to completely block or avoid updates. Generally this means opening yourself up to security concerns.