Seems to me ASA 8-8-C and 8-7-J(1) cover this. 8-8-C says:
"[Runner is not out] When more than one fielder attempts to field a batted ball and the runner comes into contact with the one who, in the umpire’s judgment could not have made an out."
If the umpire judges in your play that F4 could have made an out on either R1 or the BR, then you can't protect the runner under 8-8-C. So you must have interference under 8-7-J(1).
The only time F4 would be guilty of obstruction in this situation is if F3 had deflected the ball, and F4 was going after that deflection. In that case, as long as R1 doesn't do something intentional to F4, then F4 cannot get into the runner's path to field the deflected ball. That's covered under 8-7-J(4).