I usually just switch my user agent on my Android Phone to be a desktop one permanently. Though, that requires a browser that can do it from the Android Market or using a ROM with it like Cyanogen (or modding the AOSP browser and recompiling it with the feature). Many cases, you can just pull the browser from Cyanogen and stick it in /system/app if rooted (though I think the feature was only added with ICS).
I can't stand that popup either though and have a severe dislike for tapatalk. From my experience with administering a forum, they charge quite a bit for their software and then charge quite a bit more on top for small bug fixes they won't fix otherwise :(
One example is tapatalk users not being aware you're part of the forum staff when you're attempting to calm down some users and they go off on you. Though that works two ways I suppose, since they can't see you're part of the staff and go off on you as well and gives you an excuse to give them a couple day vacation :)
ah, i use firefox as my browser on android, which may also be mitigating some of this. Anybody who uses an alternate browser on iOS want to let us know what your experience is with the nag screens?
And it's really goddamn annoying.