I hate 2 bring an old thread back from the dead, but I wanted to pass some info on in case anyone is still having this issue as I did, (but don't as of this evening). My issue was caused by a, "Cheetah Media", app. I originally installed their, "battery doctor", app with no issues, and it still works great, (it really does extend the battery life on my OnePlus One, substantially).
I then installed their, "clean master", app which was also working fine. I later installed their, "cm security", app bc the clean master app kept recommending it, constantly. Anyway, that was my issue, and here's why, the clean master app happens to have a few of their other apps, built in, including an anti-virus app, (which I believe is cm security, or a version of it). Like I said, everything was fine, but clean master kept pushing the cm security app, even though I had a version of their security app built in. Well, I thought the built in version was not the same as the standalone cm security, bc it would be pretty stupid of their clean master app to keep recommending the cm security app if I already had it built in.
Well, apparently clean master is that stupid, and Cheetah Media, needs to keep a better eye on their software, and the apps their software incessantly pushes. Anywho, once I deleted the stand alone version of the cm security app, I was once again able to install 3rd party apk's etc. It basically boiled down to the long known reality, "that you should never have more than one, anti-virus/security suite, installed at any one time, or all hell will break loose. It has always been the case with PC's, and apparently Android is no different.
**I also thought that clean master would have been smart enough to uninstall the built in security app, before installing the standalone version, but then again it was stupid enough to recommend the standalone app in the 1st place, gaaaaaayyyyy