I am wondering this because Signal sends notifications just fine on GrapheneOS without Google Play Services but for location sharing it needs it. Additionally, how much privacy friendly is the location sharing on Signal anyways if it relies on Google?
I know this is an old post, but I'm answering for future people who might be interested.
Signal is distributed in two versions:
The google play version actually uses the google services for push notifications and location. I don't think signal has any alternative to using google services for location as this is how android with google services handles location.
The standalone version does not make use of google services for push notifications, instead relying on a dedicated connection to signal using websocket. The location is handled in the same way as above, but if you install this version on a phone with GrapheneOS for instance, without google services, grapheneOS handles location independently. If you install this version on a phone with regular android and google services, I would expect it to use location from google services because that's how google services are setup to handle location. I dont think this is configurable by an app developer, to decide do I want location from google services or not.
Hope it helps.