How would a modern day monster hunter armour look like...

Riot suit isn't good gear. If real armor did not require so many moving parts, fielding up some thick plastic in form of gothic armor would be far superior. With a bit of kevlar on top, to make it reasonable bullet resistance.
Meanwhile a lot of Police forces also field 21st century maile: So thin and strong it looks like the person is wearing woven metal.

I broke out this ancient thing from a decade ago, just for you. Appreciate it, please.

>medieval hellspawn appears as a huge horned beast, maybe in plate armor and weilding scary weapons
>modern hellspawn really does identify as an attack helicopter

what now, flyboy?

The thing with sharksuit is that sharks generally bite way softer than other "monster" tier animals. Only the Bull Shark ranks among the 10 strongest biters. Great White is no. 19 and Tiger Shark is no. 24 way below all big cart, wolves, bears and even some dogs and turtles.
A crocodile will easily bite your arm off shark suit and all because they don't depend on their teeth's geometry for damage like sharks do.

What is it about the mullet that allows it to defeat supernatural influences?

Because the mullet itself is a supernatural influence. It's just on the side of humanity.

Kevlar is decently heat resistant, especially with a Nomex layer. Realistically though it depends on the beast.

Vampire that is basically "human that drinks blood"? Normal armor is fine. Whatever.

Vampire that is full-on "I can rip you in half and pull Hellsing-tier anime stuff that will cause geisers of blood"? You may as well carry a baby blanket.

Demon that can just posses you, throw you around with telekinesis, etc? armor may be best since you may feasibly have blue-on-blue, and you have the difficult question of "do we want to pierce our own armor with AP if one of us gets possessed?"

Lich? Couldnt hurt. It'll just Disintegrate, Implode, or Wail of the Banshee you to death anyway.

Rust monster? Kevlar, MOPP suit, polymer guns, and bait 3" nails.

Dragon? Firemen suits or full flame suits, with IR MANPADS(?) and AA guns. Normal armor wont do much.

Skeleton? Use normal armor or riot armor, it'll use human weapons or melee, depending on setting.

Mummy? A priest. Nothing stops mummy rot.

>Demon
I imagine you'd have specialized warlocks and wizards putting wards on your armor before facing something that can possess you.

>Vampire that is basically "human that drinks blood"? Normal armor is fine. Whatever.
I'm pretty sure even the lamest vampires are twice as strong as a human beign. Armor won't save you from broken bones.

That's, I think, what everyone is missing here. Are you even aware of how strong man-eater animals are? Hell are you even aware how strong fit people are? Armor is not a magical anti-hurt forcefield that protects you from everything so long as you can't get cut. Crossbows and bullets put plate out of comission way before being able to puncture it because they could cave it in and leave you trapped in a hard to pull off metal vest that was now crushing your lungs and killing you slowly.

The Secret World has characters that don't really wear armor because all your protection is magical trinkets and charms.