[josephrt1]

I'll be the contrarian here. I think it is a live ball. [only speaking USA rules]

Umpire interference is with the catcher’s attempt to throw out a runner who is stealing, or an attempted pick off play.

In this example the runner is not stealing and the catcher is not trying a pick-off attempt. Instead we have a runner advancing on a dropped 3rd strike. I think that is a difference. Umpire's interference only applies on a steal or pick-off. Any other situation where the umpire gets in the way, its a live ball.

So I think, live ball. R1 and BR could even try for more than the one base. Umpire screwed up but its part of the game.

This scenario could be simplified. No runners on, no outs, DTS. Catcher picks up ball, attempts to throw to F3 and umpire bumps the throw and it goes into RF or goes into stands. What do you do with BR?