Hi mdooley,
as a side thought, it might also be theme related?, what theme are people using?, I don't have a problem with traditional layout using Ambient Mate Dark theme with Pocillo icons and Chameleon White Large pointer!. I use the same on 3 computers now (I installed UM on a 3rd PC yesterday). 
Resetting the panel didn't work (I also tried it before posting here). Strangely enough, the problem seems less and less frequent now. I can't remember last time I saw two icons in my status bar. Anyway, I see other people also have the problem so I encourage everyone to add to the bug report that @layingback started. As I see we haven't received an official answer yet.
Just tested this. Restarting network manager did not help.
Same issue on my side. Here some additionals informations. With my nvidia desktop 18.04, it was rarely, about one times by month. Since 20.04, I got just one times. Both about network icons, redmond style. With my laptop full Intel still running 18.04, I didn't see that issue (same redmond style, same theme as desktop). The other big difference between my machines, its the use of openvpn on my desktop. Also, I know dbus is used about some icons indicator. May be it will interesting to further more investigate in these way?
The solution is to twoo nm-applet icon (with bionic work for me )
Add 2 seconds delay to startup to nm-applet
I have the same issue. How did you add a 2 seconds delay? Can't understand the photo you attached! Thank you!
Unbelievable! This works 
The duplicate network icon was there for years now... But now I have only ONE network icon 
Thank you 
I had the same problem. Set startup delay on Network resolve it. Thank's
I had this problem in Ubuntu Mate 21.10 and this suggestion solved it. Thank you.
