I have been stuck on the "acquiring user location" screen for a while, and I know for a fact that my device's GPS does work in other apps, such as Maps and My Tracks. How can I bypass this screen?
If this happens only sometimes, you might try restarting the app from the beginning. This should restart both the GPS location fixing process and the game's knowledge of current GPS status.
When you switch applications on Android, they are not always entirely closed (they go to a "stopped" state, from which they will be destroyed when the system wants to). This allows to resume the applications quickly, but if the application is in an error state, it also resumes the same error state.
To force close an application on Android:
Go to settings, active applications, and click on the "end" button to stop it.
On new latest Androids, it's also possible to use the application switcher (long-press on home button). When you slide an application off the list, it gets closed.
You'll know ingress was completely closed, if when you open it, it starts with the short splash screen showing a version number and a logo.
However, if this happens all the time, seems like Ingress application can't connect to your GPS for some reason. File a bug about it, if you've confirmed that other applications can get a GPS fix.
You can use the Back button to switch to the main game screen.
However, this answer will not help you in any way. The whole point of Ingress is to walk around (even though some people drive …) and hack portals. For the most part the game mechanics depend on your precise location; Ingress (mostly) refuses to work when it cannot acquire that.
You cannot do anything with Ingress on a phone without working GPS. So why bother?
The screen can be bypassed by pressing your device's back button, which will take you to the main screen.