As soon as this starts applying (when it initially starts resolving, or applies again after being negated), players send monsters to the gy.
After that, if you have monsters with the wrong Attribute, they are destroyed by game mechanics. While you control a face-up monster, you can:
Tribute Summon a monster using your only face-up monster, even if it has the wrong Attribute. (EG: Your only face-up monster is "Treeborn Frog". You can Tribute it for "Caius the Shadow Monarch").
Take control of an opponent's monster with EG "Brain Control", even if it has the wrong Attribute. (If it has the wrong Attribute, it's immediately sent to the GY).
Summon/Set monsters face-down, even if they have the wrong original Attribute.
If you control no monsters, you can Summon multiple monsters with different Attributes at the same time. (After they're summoned, send monsters you control to the GY so that you only control 1 Attribute). While you control a face-up monster, you cannot:
Ritual/Fusion/Synchro Summon a monster with the wrong Attribute, even if you would use the monsters you control as tribute/material. (EG, you can't use 2 Sea-Serpents to Synchro Summon a Psychic).
Flip/Normal/Special Summon a monster with the wrong Attribute. If a Set Monster is attacked:
It's not sent to the GY until After Damage Calculation.
Its Flip Effect will activate, but it is not "destroyed by battle" (EG, Shura and Mystic Tomato will not trigger, since nothing was destroyed by battle).
Monsters with multiple Attributes, like "Light and Darkness Dragon" are sent to the GY when "Gozen Match" resolves.
While "Gozen Match" is face-up on the field, you can Summon monsters with multiple Attributes, such as "Light and Darkness Dragon" or "Elemental Mistress Doriado", but they will be immediately sent to the GY.
You can take control of an opponent’s monster that’s the wrong Type/Attribute with a card like "Mind Control". If you do, it’s sent to the GY immediately after you gain control of it.
While "Rivalry of Warlords"/"Gozen Match" is active and you have a face-up monster, you cannot Summon monsters that are a different Type/Attribute from the monster(s) you already control.
While "Rivalry of Warlords"/"Gozen Match" is active, you can still Set monsters of any Type/Attribute, and you can Special Summon monsters of the wrong Type/Attribute face-down. But you can’t Flip Summon them afterwards, and they’re sent to the GY after damage calculation if your opponent attacks them. Also, in that case, you won’t get the effects of cards that need to be destroyed by battle and sent to the GY, because they’re sent to the GY by the Trap Card’s effect instead. But Flip Effects will still activate.
However, if you have no face-up monsters when the effect resolves, you can Summon any Type/Attribute of monster.
If you control no face-up monsters, you can Summon a monster of any Type/Attribute.
If "Rivalry of Warlords"/"Gozen Match" is being negated, you can Summon monsters of any Type/Attribute. If it stops being negated, you have to send monsters to the GY until you control only 1 Type/Attribute again, just like if "Rivalry of Warlords"/"Gozen Match" had just resolved.