Your saves from v1.3.1 are NOT compatible. Your hats and settings are fine, though.
New Features:
-You can now type "secret" into the console to get hints for how to find secrets and secret hats in the current level.
Fixes/Changes:
-Fixed side quest UI bugging out in multiplayer again, but in a different new fun way.
-Fixed Boss Melon getting stuck in falling animation if an invincible entity gets under the boss while it is jumping.
-Fixed hat unlock script sometimes not giving hats to players under certain conditions.
-Fixed getting softlocked inside of the Fridge of Death in level 2.
-Fixed some texture misalignments in the difficulty select level and level 1.
-Improved compatibility with the Corruption Cards mod.