Android Auto supports arbitrary resolution sizes. If you go through the effort of setting up the android IDE and AA emulator you can see this for yourself.
First off, this is a great initial test to do; Rule out the big stuff early. But, the way most will probably read this is that Google/Android Auto supports portrait aspect ratios and thus it must be the infotainment supplier that hasn't chosen to support it yet. There are a couple potential issues with that assumption. First, just because the Android Auto
emulator (i.e. the client receiving displaying the AA content sent to/from the phone) supports this feature, it doesn't necessarily mean that the spec has been distributed to the hardware suppliers. I just looked around and it appears the Android Auto protocol (over USB) is not public and so each of the infotainment suppliers likely have a license contract with Google. Even if Android itself supports AA portrait ratios, the legal department may not have decided how they want to test/certify head-units for compatibility in non-landscape ratios (or dozens of other non-obvious hang-ups like that).
Second, Google's Android is not the same Android that most people have. When you download their SDK and run their emulator you're demonstrating the very latest "stock" Android, which may support portrait ratios just fine. But it's also possible that OEM (e.g. Samsung) and even phone carrier modifications to Android are either too old to include that support, break it, or just make it unreliable enough that it's not OK for the infotainment manufacturers to support it.
EDIT: If someone is motivated enough you could check if either
OpenAuto or
AACS, both of which rely on a reverse-engineering of the AA protocol, support specifying portrait aspect ratios. In theory you could use a real (e.g. Samsung) phone with real 3rd party apps and at least see how smoothly it goes with actual customer devices outside of the stock Google emulators.