There’s actually an option to turn GMS off entirely if that’s a concern (Settings–>About–>Advanced). It comes at the cost of slightly increased battery usage. Sadly Google does have a bit of a monopoly on mainstream Android there.
Having said that, the messages themselves should never pass Google’s servers, just a packet saying “check your Threema server, there’s new stuff waiting for you.”
There’s actually an option to turn GMS off entirely if that’s a concern (Settings–>About–>Advanced). It comes at the cost of slightly increased battery usage. Sadly Google does have a bit of a monopoly on mainstream Android there.
Having said that, the messages themselves should never pass Google’s servers, just a packet saying “check your Threema server, there’s new stuff waiting for you.”