Even newer phones like the Motorola Moto G 2015, which was one of the first phones to get the Lollipop update, has issues connecting to an Android Auto system. And that's official now because Google themselves have acknowledged the problem on their Support page.
If you head over to the Android Auto Support page and scroll to the bottom, you will see a section that says "Known Issues". This is what it says...
Motorola Moto G
Android Auto doesn't start on the Moto G. We're working with Motorola on a solution.
The footnote has been up there for close to ten days now with no fix in sight. I've been searching forums threads across the internet and there are many users who have confirmed the issue still exists.
Some users have been able to get their Moto G devices to connect with Android Auto on aftermarket Pioneer head units. Others have complained about Android Auto launching the first time they connected but subsequently failing to connect after the phone freezing. Either way, it is best to wait for news from either Motorola or Google about a fix.
This Moto G screenshot was posted by user 'Pedrore' on Android Central Forums...
Top image source: Motorola