The best software doesn't need to be trusted because it's open source and self-hosted.
I haven't looked into this in a while but I believe the current Beeper app only allows you to use Beeper servers, is not open source, and requires you to connect it to a Google account for unknown reason, for those reasons, I say no.
The previous "Beeper Cloud" was open source and you could theoretically self host it and run it on your own server. Probably still can.
But I stopped using it for a completely different reason:
Its intended to do something that the services it uses DO NOT want you doing. For that reason, they make it intentionally difficult to do. Apple demonstrated this really well when they predictably "patched" the iMessage loophole PyPush found. You'll be logged out constantly, there are constant bugs caused by server-side changes, and your accounts will be flagged for "automated activity".
Any convenience it's supposed to give you is just negated by these complications.
I just looked into it again out of curiosity. It no longer requires a Google login (nor does it even require Google Play services, because I don't have them. This will probably change once they go paid, which they've apparently rolled back since the iMessage debacle).
It says it supports SMS/RCS, but it actually supports neither. All it does is connect to your Google messages web account. This is an absolute joke for an app that bills itself at the top of it's home page as "all your chats in one app" and it doesn't even support the most common chat method.
As far as I can tell the app is still closed source.