Is it a requirement to downgrade the game, because the downgrader makes my game crash on startup.

Did you follow the tutorial made by DarkViper? Theres also an alternative method for downpatching your game: https://www.speedrun.com/gtav/guide/gpgmb

I cannot read any rule that states you are forced to run on an older patch, so I believe its not a requirement.

I don't run GTA V myself but I believe there are certain advantages running on Patch 1.27 like having no waves in the water and probably certain other advantages I myself am not aware of. If you wanna know for sure you should probably hop into the Discord and ask this yourself.