Reddit mentions of Scosche FM-MOD01 Modulator Play Satellite Radio Tuner, or Other Portable Music Player Through Any FM car Stereo

Speaking of which, even if your car stereo unit doesn't have one of these dedicated CD changer or satellite radio connectors, there's one solution that will work with any FM car radio and isn't a short-range transmitter: an RF modulator (FM modulator).

This is what early aftermarket CD changers used. Rather than broadcasting an FM signal over the air, the modulator gets added inline with your antenna lead (antenna lead plugs into the modulator, modulator plugs into your radio's antenna jack), so it can insert your aux line input as an FM radio signal directly through the antenna lead itself.

They're so limited in transmit power that they're never great if there are a lot of stations nearby.

What you want instead is an FM Modulator which converts the signal to an FM "broadcast" the same way as the transmitter-- but instead of transmitting it super-weakly, it plugs directly into the antenna port on the back of your old car stereo and sends the signal down the wire straight into the receiver.

You can get an fm modulator like this, which takes the antenna line and adds your aux connection as a station on the radio, and all your other stations will still work as well.

Three ways to do this, from merely okay to great...

1. FM transmitter. Will probably work, but results can be hit or miss. If you live somewhere where there's a lot of radio stations, it can be difficult to find a frequency where there's no interference.
   
2. FM modulator. Something like this will work: https://www.amazon.com/Scosche-FM-MOD01-Modulator-satellite-portable/dp/B0007THIDQ You'll also need antenna adapters since VW don't use the universal plug. I used something similar to get an iPod into an AM/FM radio for years. Much better than a FM transmitter since it's hard wired to the radio, and completely disconnects the antenna when it's in use do you don't get channel interference.
   
3. Aux adapter. Much better, since it talks directly to the radio. Something like this: https://www.crutchfield.com/p_249BTSVW2/Crux-BTS-VW2-Bluetooth-Interface.html Some of these allow any radio or steering wheel control to work with a blue tooth device for track skip, etc.

FM Modulators work great, avoid FM transmitters like the plague.

If you're hell bent on Aux installs, and want to keep the factory look, consider an in-dash FM modulator (like this one).

The way I see it though, joshuamnr is right - you should ditch the whole Aux idea and go bluetooth, because the quality is way better, plus it's a nice upgrade. I know that BMW head units are complicated though, and fits are not easy. I had a pioneer AVH series in my Jetta and I loved it - quality was awesome, and the screen was easy to see in the sunlight.