Sudowoodo

Say my opponent has a Sudowoodo with the "Roadblock" Ability on his bench, but it's currently disabled due to my active Alolan Muk's "Power of Alchemy" Ability. If I have five Pokemon on my bench when Alolan Muk gets KO'd and "Roadblock" becomes enabled, do I have to discard one of my five benched Pokemon before promoting a new Active Pokemon or not?

When you remove your Active Pokemon after resolving all effects that caused it to be KO'd, you must replace it immediately before resolving any other new effects that take place.

My opponent and I both have Sudowoodo with "Roadblock"Ability in play. I use Hex Maniac on my turn to shut off "Roadblock", and then I play 5 Pokemon on my Bench. My opponent plays 5 Pokemon on their Bench during their turn. At the end of my opponent's turn, Hex Maniac's effect ends, so "Roadblock" activates again. Who discards their Pokemon first? If the first player discards their Sudowoodo, would the other person need to discard a Benched Pokemon?

It's the opponent's turn, so their Roadblock goes into effect first. You would discard your Pokemon first, and then your opponent would discard theirs. Even if you chose to discard your Sudowoodo, your opponent would have to discard down to 4 Benched Pokémon because the Roadblock effects happen simultaneously.