I'm one of those exceptions that deviates from the norm: I run CyanogenMod without any Google apps.
Is it possible to download the Stack Exchange Android app .apk directly?
Currently our application is heavily reliant on Google's add-ons. We use two-way Google Cloud Messaging, Google Sign-In and more.
At this point we don't think it would make sense for us to test everything on both regular phones and phones without Google's add-ons installed due to the fact that we'd have to double our testing to support a small minority of users. Not to mention the headaches caused by manually giving out APKs since we lose the automatic updating features or even update notifications at all. If this becomes a bigger issue, we'll obviously rethink this.
At the moment our official stance is that if you can somehow get the APK to your phone and get it to not crash, that's fine go ahead and use it, however we won't be supporting it.