I am getting this screen too. I want to use my phone in place of my flash drive and do not want to have to tap anything.
be particularly important when I want to access my data when my battery is dead. But then, perhaps I would not be able to access the SD card when my battery is dead even if I had auto mount.]
Leaving the dead-battery situation aside, I want to be able to plug in and go, without touching my phone or even taking it out of its bag.
So, in apps there are
I don't want winamp, but it has a setting to allow automounting when I connect USB. The screen still appears (which is a pity) but it is as if Winamp pushes the allow USB access button for me.
Auto Mount SD card
looked like it would do the trick but it is icompatible with all my devices.
Multi Mount SD-Card
may need "root" and my device is not rooted. I am not sure if root is needed or not. In order to find out I have to pay a dollar. This is a bit iffy. The app warns me that some functions won't work without root access and then invites me to pay a dollar not mentioning whether that function is one of the ones that requires root access or not. Well it is only a dollar.
doubleTwist with Magic Radio
Is, I think, an iTunes android integrator (which I do not need) but it said to have the ability to turn on automatic mount and is recommended by lifehacker as a way of getting auto mount. But it did not work for me by default so I un-installed it.
On the developers forum there is the suggestion that automounting was only possible on android 1.0 and that it was a bad idea.
I am using NEC Medias Tab N-08D running Android 4 ("Ice cream sandwich"?). Perhaps I need to root my device. I have no idea how.
Since my tablet is also a phone with 4G connection I guess that root access may allow me to do things that I am not meant to do on the network.