Webroot suggested I 'allow' Firefox under Identity Protection → Application Protection. I found four instances of Firefox in the list of applications, which I changed from 'Protect' to 'Allow'. After doing that, I can have FF and Task Manager open at the same time without losing control of mouse and keyboard input.
Earlier, I'd tried allowing taskmgr.exe in WR but that had no effect.
Other info: The TM problem initially affected Chrome as well, when Creators Update first installed. Current Chrome build isn't affected on my PC although there are many instances of Chrome in the Webroot app protection list, all set to 'Protect'.
Also, I've had an issue with WR Identity Protection before with another programme, WriteMonkey. Copy and paste stopped working after a WriteMonkey update. I eventually tracked down the cause to WR Identity Protection. Again, 'allowing' WriteMonkey cured the problem.
Thanks for posting this. Doing as you suggested fixed the issue on my laptop, but I also had to "allow" cryptsp.dll on my desktop in order to fix it. Not sure why - I just played around with "allowing" everything that was protected there until I narrowed it down.
Edit - I discovered that I can "protect" Firefox. I only have to "allow" cryptsp.dll and am working fine again.