I just got off the phone with my parents who experienced this symptom with considerable concern. They had noticed a new "From" email address selectable when composing a new message on the iPhone. The email address was apparently two randomly selected works and ended with the domain @my.minbox.email. The installed Profile in Settings>General was something along the lines of "MyWeatherRadar Click Install for your FREE Weather Radar Alerts!"
I had them look for the potentially offending applications, and suggested just deleting all third-party weather-related applications. I then instructed on how to remove the unwanted Profile.
What I have determined so far is the bogus Profile is what's called a Provisioning Profile normally used for installing beta applications outside of the App Store as well as for provisioning phones for employees in an enterprise environment. New profiles may be delivered via an installed app, or possibly, downloaded via Safari. In either case, the phone is to take the user to Settings, show the profile with an Install button. Tapping Install should prompt "Install Provisioning Profile: Installing this provisioning profile will change settings on your iPhone. [Cancel] [Install Now]"
A clue to me is the name of the provisioning profile including the words "Click Install for your FREE..." To anyone not familiar with the ins and outs of iOS development and security issues, this sounds innocuous enough.
Provisioning Profiles seem to bestow all sorts of capabilities, such as creating new accounts, installing new root certificates, and in the wrong hands, posing a certain security risk. Applications which install a new root certificate theoretically have the ability to deep-inspect network traffic or even inspect / modify network traffic by setting up a proxy server.
At this point, I'm unsure whether to advise my parents to change their iCloud passwords just to be on the safe side, but probably prudent. In the mean time, I will educate my friends and family to be careful of any website or app that wants you to install a provisioning profile on your phone. Just don't, unless you know exactly why you are doing so.