Interference/Does the run score

[DownTownTonyBrown]

I'm with ChampagneBlue... somewhat. This sounds like incidental contact.

When was the contact between BR and F3? And where were the runners?

After the throw had arrived and been missed by F3 - incidental contact. Play on.

Before the throw arrived and the contact caused F3 to miss the catch - interference, BR is out, runners stop advancing at time of interference and must return to last base touched (runner from 3rd may have already scored - count it).

If the contact was intentional then based upon the severity and its timing, I might:
Send runners back to 2nd and 3rd, BR out.
Eject BR for malicious contact and stop play at time of interference - possibly allow runner from 3rd to score. Maybe not, too.
Call dead ball and leave BR at 1st but call runner from 3rd out for the BR's interference and the defense's potential play at home.

Anything besides the first two possibilities will require decisive umpire judgement and confidence to sell those out of the ordinary calls.