Do some apps prohibit mirroring through VGA? I have an iPad 2, which was running iOS 5.x. I could mirror every app on a TV using a VGA adaptor. I recently upgraded to iOS 8.3 and, unbeknownst to me, the new OS's default settings also updated all my apps. Now I find most apps still mirror, including YouTube, but a couple apps (the kind requiring a monthly fee for streaming video content) no longer mirror video content.

I've looked here and elsewhere to figure out what's going on, but it's confusing. Did the content providers behind the apps change their policies about projectable content recently? Are the apps now providing content at a resolution too high for a VGA connection? ... Most importantly, of course, do I have any options to once again mirror these video outputs to a TV screen?
Short answer: Yes.

Some Apps (usually those with paid content) prohibit video output via AirPlay or AV-Adapters. There's no way I know of to get around the issue. 
For some, not all, a HDMI adapter works because of "High-bandwidth Digital Content Protection"