The following two citations are for OBR but I am certain they also apply to FED. The 2017 Jaksa/Roder manual says, “If a batter-runner is obstructed before first base, but his batted ball becomes caught or foul, the obstruction is nullified.”
The 2018 Minor League Baseball Umpire Manual states the same thing (section 6.16, p. 95):
When the batter-runner is obstructed before reaching first base, it is not always the case that the batter-runner will be awarded first base on this type of obstruction. For example, if the batter-runner is obstructed before reaching first base on a fly ball or line drive that is caught, the batter-runner is out. The reasoning here is that the obstruction had no bearing on the fact that the batter hit a fly ball that was caught by the defense. Similarly, should the batter-runner be obstructed before reaching first base on a foul ball not caught, the foul ball prevails. Again, the reasoning is that the obstruction had nothing to do with the fact that the batter hit a foul ball.