If you've asked yourself "how do I activate these modes" than here is the answer. Add the following parameters to your Carmageddon: Max Damage desktop shortcut:

-pedsubstitution trumped_up.txt -> (for Trumped-Up mode)
-pedsubstitution hillarious.txt -> (for Hillaryious mode)
-pedsubstitution mass_debate.txt -> (for Mass Debate mode)

Example: "...\CarmageddonMaxDamage\bin\Carmageddon_Max_Damage.exe -pedsubstitution trumped_up.txt"

At the moment there is no ingame option available to activate these modes. Hopefully that will change through another patch in the future (no guarantee).

It can also be done by using custom settings in GOG Galaxy. Details in this thread:

https://www.gog.com/forum/carmageddon_series/carmageddon_max_damage_1