I just want to share my findings. Whether some way to prevent this in replay mod is created or not, I just want to be helpful to anyone having a similar issue.

Context

A server I play on has a custom resource pack. For an unknown reason, last month, that resource pack would crash my game. So I just told Minecraft not to load that servers resource packs anymore. This is the only servers resource pack that does this.

Problem

Replays that were saved, when the resource pack was working, are also crashing the game in the same way. Every single replay that was saved with this resource pack are effected.

Solution

1. Download 7-Zip
2. Go to %AppData%\Roaming\.minecraft\replay_recordings in File Manager
3. Right Click on the replay with the bad resource pack --> 7-Zip --> Open Archive
4. Delete the resourcepack folder and close 7-Zip

I hope this is helpful to anyone else having this problem.

Possible Mod Fix

Similar to the Edit menu on a Server (in the Multiplayer Menu), the Edit menu on a Replay should have an option to disable saved resource packs.