Relationships (of all kinds) are about compromise.

Exactly. As I have understood, she is not willing to use an other messaging app. It seems as if only you are ready to have a compromise.

to the extent that us nerds do

This is not “not caring to that extent”. This is not even just not caring at all. This is straight out ignoring and nullifying any and all concerns of one of the parties over privacy, by the other one.

So you can choose to be dogmatic in your approach

The only dogmatic thing here would be to say “only matrix”, or “only signal”, or whatever. As I understand you have attempted to offer multiple options.

people in the world who don’t care

It’s mostly irrelevant if they care about it. In a healthy relationship no one is The Boss whose decisions must be accepted. Instead if one party does not care about something, but the other very much does, they can accept that and live with it, if that’s not a terrible choice. For example if your wife does not want to eat meat, would you force them to do so, because you don’t want to deal with making meatless meals? I often eat meat, but I would be ready to give it up regularly doing so if need be. Or if they don’t want to deal with the selfhosted media store, ok, fine, let her keep her Netflix subscription. This however, is not about pleasures, but about giving up or not human rights important to me.

In this situation however, it sounds like as if your girlfriend with be “The Boss”