One of the most annoying situations was when I had a great podcast I wanted to share with someone on a long drive, pulled out the iPhone 7 to plug into their car stereo and.... new-ish car.... but AUX only.... no dongle..... never mind!
I believe Apple removed the headphone jack 5 or 10 years too early. Bluetooth is not that great, and it's also not that widespread. AUX is not a floppy or CD drive, it is everywhere and works great and allows for high quality audio, no troubleshooting, no compression, no hassle. The alternatives (dongle? Bluetooth?) is comparatively nowhere and does not work great.
Personally I bought Bluetooth headphones and that's it, imo people are being too dramatic about it.
Problem solved. Enjoy
I'm using a 1,5€ BK8000L module (http://www.electrodragon.com/w/BK8000L) that I soldered to my old stock autoradio, replacing the tape audio circuit, and the quality is much better than FM.
Of course if the person is willing to attach something to the car audio as you have, that's the best!
I didn't think about that, yeah, but the OP said they had an AUX input, so quality should be good with a (even cheap) bluetooth adapter on that.