Fielding is normalized against both the pitcher on the mound and the batter at the plate. This link will help you see the impact:
https://www.whatifsports.com/mlb-l/league_averages.asp
RRF is sort of normalized, it’s a custom WIS formula which is why a players RRF won’t match their RF/G or RF/9 on B-R.com. Think of it more like an RRF#. Which is pre-normalized against a historic average pitcher/batter combo.
Fielding is normalized in the game as described above, which is why you don’t usually see large variances on player RRF vs RL RRF since it’s displaying a pre-normalized value. The batter/pitcher matchups that are faced in actuality will still swing it, but since it’s set at a relative midpoint, it won’t swing as wide. FLD for deadball players will often swing wide (better) if they’re regularly behind modern pitchers facing modern batters, and similarly, modern fielders will swing wide (worse) if they’re behind deadball pitchers facing deadball batters.
Fielders with same grade will perform roughly the same with opposite era pitchers/batters.