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I'm not sure how well you understand how GP Services and GCM works. My understanding is not complete but I'll explain a few things:
Notifications:
From what I understand to get notifications you have to install GP services (and maybe Playstore), and they need to have internet access. If you are gonna install these two then you might as well install GSF for complete compatibility, but you might not have to.
Any app that uses notification will only detect the presence of google components if its installed AFTER those components were installed. If installed before then the app will notice the non-existance of the components and either resort to its own independent notification system (batter draining) or will give a warning and not work. An app will not "change" this position later, unless if reisntalled.
Once an app decides to rely on GCM for notifications, if the google components are then disabled or have no internet access then GCM will not work and the app wont receive any notifications.
Privacy:
Signal uses GCM if present. I've read that the way signal uses GCM does not expose your messages (content). Though i am not 100% sure on the phone number. I don't quite remember what it does expose, perhaps you can research.
Privacy respecting opensource apps generally do not expose any information to google components, so its generally the case that installing these apps in a profile that contains google components doesn't expose any data contained in these privacy apps. The reason is that these apps do not use GSF and don't use shared analytics with GP services.
The privacy problem mostly arises when you combine apps that normally DO use google components and IPC with a profile that has google elements installed. Then there is a chance of leaking data between these apps and google or other analytics companies. Also the risk of sharing data between such apps arises.
For example you may have installed the google elements in a profile but not be using any google account to log in (preventing identification). If you then install and use an app that DOES KNOW your identity (such as email, phone number, credit card, etc) then these apps could share your identity with the google instance.
Also installing any google apps such as gcam or gboard on such a profile could theoretically leak some private data to the google components.
Now in the case of signal, signal might not expose your phone number to GCM or the google components (though i am not sure of this). However installing whatsapp likely will. Telegram also might do that. Installing payment based service apps (door dash, uber, banking, etc.) or other popular Identity based apps could also share data with google through the google components.
One solution to deal with the privacy problem is simply to disable the google components after install or prevent their internet access. This will allow app installation compatibility and allow the apps to work, but the notifications wont work. Although there is still some potential of the Google component instance IDs to be detected by the apps and shared directly with analytics companies and cause cross contamination.
Another solution is to install the invasive apps and the required google components in a dedicated profile where such data exposure is considered OK and unavoidable. Then separate apps like Gcam and gboard can be installed to a different profile so that they don't get connected with those other apps. Google maps is another example where having it isolated in a profile would be helpful in isolating your movement data from being associated with other google components.
The best way to proceed is really dependent on what apps you need to have and what works for YOU. A strategy is therefore required in order to limit and and compartmentalize groups of data and what gets shared with which app. This strategy has to necessarily be tailored to the individual user's needs and priorities. What is required is a good understanding of how data sharing between these components works, which I just expalined to you.
Its a bit complicated as you see.
So to sum things up:
- privacy apps generally can be installed anywhere and that's usually fine.
- the "colluding" apps are where care must be taken to avoid unwanted data exposure.
My explanations might lack some detail, which perhaps other users can chime in on, as I am not fully educated on every detail.