Edit: I figured it out. The problem wasn’t permissions or Firefox itself, but my launcher. I’m using OLauncher, 'cause I rather like it’s text-lookup interface, but as it doesn’t make use of a traditional “home screen” Firefox won’t allow me to create an entry there.
Apparently, it’s a much-desired feature request
I think it may have been renamed to “Install” in previous versions, but neither appear anymore, and I don’t see any permissions denied so I’m assuming that can’t be it.



HTTP Shortcuts on F-Droid does it better with better control IMO. This is what I use now.
For anyone else wondering F-Droid Shortcuts
Not quite what OP is asking for, seeing as they just want to open the site in their browser from the home screen.
But anyway, it’s funny how that app has somewhat advanced scripting features a-la Tasker, but built strictly around firing http requests.
It does open websites in their browser from the home screen. I wouldn’t have recommended it if it didn’t do that.
You can even get it to open in a specific browser instead of the default browser.