Yes, there are privacy groups of different kinds.
Try it, it's not as hard as some people say, the onboarding and interface has been refined.

Look for "Simplex directory" and search there for groups.

The only sad thing is that it's centralized, kind of signal but better.

On the privacy front I believe xmpp + omemo shines, and jami is also very interesting (though jami for some reason is doing efforts to allow LLMs agents and bots, through plugins of course not by default, but I don't see the need of any of that stuff on something like jami). Sadly briar is on maintain mode and it was really bad on phones' batteries, tox never took of leaving only jami like a viable distributed alternative. xmpp is decentralized and federated, doing pretty well with omemo...

I dont use it because of the lack of moderatoon tools for groups.

Also main groups are filled with transphobes and fascists, with moderators there doing nothing.

Yes, but there were three gotchas that make it difficult to use for our purposes - one is that you have to have your phone on and connected if you want to use the same account on another device. Given I use my phone as much like a dumb phone as possible and turn data off when I don't need it (aka most of the time) it's impractical to use. We kinda got around this by having different accounts for different devices bit it left you guessing which account to contact someone on because you don't know if they're on their phone, laptop, PC, etc.

It uses a a chunk of battery and the devs seem completely disinterested in UnifiedPush.

A lesser but helpful feature that's lacking is web chat. It's a lot easier to get family and friends sold on alternate chat clients if they can try it out using a web browser they already have instead of installing yet another app.

I'm curious why you would be interested in public groups on Simplex? Its great for direct messages and small friend/invite only groups. But what would you gain in terms of privacy with public groups? If the challenge to entry is "click this public invite link", you should assume bots are joining and scraping anything with triple digit member counts. If your threat model is focused on corporate surveillance, public group chats aren't that much different than community forums that lack a bot friendly API for scraping. Which is to say, very easy to scrape still if anyone actually cares to.

As others have mentioned, the moderation tools are basically nonexistent and bigotry runs rampant. Even if you try to organize alternative groups to the Nazi bars, you will not have any tools to stop organized harassment.

SimpleX is an encrypted instant messaging app, it's not designed as a social network or a forum.

Large group members often suffer from unreceiving some messages, due to group encryption complexity. It's almost like the famous "unable to decrypt message" in Matrix. Maybe one can create an unencrypted group, but then it makes no sense to use SimpleX.