Why am I getting Universal Clipboard popups when I'm not typing anything? I was just in the Weather Underground iOS app on my iPhone.  I was not inputting text, I had just opened the app so it was showing me weather conditions for my current location.  After the app finished loading all the weather info, I got the "Pasting from [my MacBook's name]" dialog that I usually see when I'm trying to paste something I copied on my MacBook.  I believe this dialog is part of Handoff/Universal Clipboard.

To reiterate, I wasn't inputting text in the Weather Underground app.  I was not pasting.

Does this dialog mean that the Weather Underground app read my clipboard?  Or is there some other explanation for why I would get this dialog when I'm not obviously trying to paste?

Perhaps I'm a bit late to the party here, but I am suddenly concerned about the privacy of my clipboard in iOS apps, particularly when that clipboard might actually be coming from my MacBook.  And weather apps are no stranger to privacy problems.
You are likely correct. If you get a UI that says that the system is "Pasting from [my MacBook's Name]", then this likely means that the application in the foreground of your iPhone is reading from the universal clipboard.  It is unlikely that it is being read by another program in the background. So it is likely that Weather Underground is attempting to read from the Clipboard.

See:
* https://support.apple.com/guide/mac-help/copy-and-paste-between-devices-mchl70368996/mac

My suggestion is that you test by doing the following:


Repeatedly copy something on your macbook, kill the Weather app, then exercise the weather app. 
Take your Macbook off the network and repeatedly run and kill the Weather app.