Is there an alternative to Android Auto that doesn't share everything with Google?

I don't think Apple cares about privacy, I think it's just a convenient selling point since they don't have an advertising program. That said, they are less intrusive than Google by a mile.
Yeah if privacy is a concern I seriously doubt Apple products are a good answer.
- I think they weren't implying it's the best option, just that it's the lesser evil. You can definitely go for some other foss options or a separate satnav entirely, but Apple Carplay works on most cars without requiring additional software or tools. Obviously OP will have to buy an iPhone.
I use organic maps and it has worked great for me. I believe it uses the same map data as osmand so they should be effectively the same, but I like organic maps enough that I feel its worth mentioning.
- Thank you for mentioning this, just tried it and will be using it!
I'm not sure you're being downvoted just because of the Apple dislike nor because of Apple's blatant disregard to our privacy, but, instead, for answering 'Apple' when the OP asked about 'Android'. Maybe a little for calling us 'goobers' hahaha

There's OpenStreetMap for maps, and Bluetooth audio for music.

There’s OpenStreetMap for maps
What alternative to Android Auto is compatible with OpenStreetMap? Since OP asked for an alternative, and what maps app works with that alternative.
- Organic maps, is what I use.
- I mean placing your phone in one of those car holders or having someone else hold it. It may not be entirely as convenient as having it displayed on a built-in screen, but it's Google-free and works. I don't think there are any full software alternatives, because to my knowledge, the car has to allow apps to access the monitor, so you can't just have any app there. Whatever other things Android Auto does, you should be able to do with just your phone.
  I guess the alternative is to get something to hold your phone in place.

Android head unit that doesn't have mobile data. You'll basically have a full phone in your car but it doesn't have any way to connect to Google

How does it connect to maps and streaming services then?
- They can tether to your phones data

A car sat nav, and something like GrapheneOS does hands free calling. Not sure if you can sync music through it as I haven't tried yet.

I think the individual items are probably workable, but an integrated experience, possibly not.

Even car sat nav is an iffy subject. If you car has a data connection, there's good odds that someone is harvesting that data.
For example, I've heard GMC happily sells OnStar data to the lowest bidder - it comes anonymized and aggregated but it's hard to believe they aren't collecting it in a less anonymous fashion.
- How about Garmin?
  Their Smartwatches are recommenced in Mozilla's Privacy Not Included. I cannot imagine their sat navs have an issue. Especially older models.

It's not a 100% solution, but many head units will have hdmi input, but you might have to accidentally install the head unit in a way that bypasses the parking brake interlock for it to work while driving. Most phones can utilize a USB-C to hdmi adapter for screen mirroring, although touch data won't be sent to the phone.

Apple Car Play won’t share anything with Google as long as you don’t use Google apps on the iOS device. 🤣
Edit: meant to reply to OP.
- Just curious, can Google apps still do cross app tracking if you check the do not track option on ios devices?

yea its called a map and CDs

And refolding a map is easier than navigating those psychotic infotainment thingies.
A cheap 32gb MP3 player hooked up to the AUX port on your old car radio is almost as lo-tech as CDs but allows you a much much easier experience.
I keep a GPS in my car in case of emergency, but I try to plan my trips ahead by memorising landmarks on OSM. As a species, we are losing our navigation skills.
- We used to cross Europe with just a small piece of paper attached to the dash with the names of the cities we'd roughly cross and it worked.
- i fesl you

There is no real alternative Only kinda alternatives by having a private maps Application

I think your best bet would be to get either a head unit that has full android on it or an Android tablet and then side loading the apps you would like to use

a head unit that has full android on it
Is that still a thing these days?! I feel like I haven't seen one in many years. Everything seems to just integrate Android Auto instead.
- I'm sure it's still possible on certain cars, but they're getting harder and harder to find as more and more companies move from the standardized head unit sizes and over to the tablet-style interfaces.

If you want an integrated setup you can either roll your own in car computer or use the apple stuff.

If you can tolerate the 90s style system then a secondhand gps (do your research) and an mp3 player connected to your stereo and the little clip that holds your phone in front of the vent works.