The shooter gets far less blast than a bystander off to the side but I digress:
I have a friend who is over 70 years old. He was in the National Guard here in Idaho many years ago, in an artillery group. He tells me they used to open their mouths when standing next to the big guns, for the reason stated.
Having heard this, I tried it when standing to the side of a 50 cal with ear muffs on. Didn't seem to matter-- it was very unpleasant either way-- it had a muzzle break you see...
Technically, I don't see how it could "equalize the pressure" unless your eustachian tubes were open. I can open mine at will, but I can't say I've ever tried it at the gun range to test the myth. Certainly, this would closely resemble the technique used by microphone designers to cancel out certain frequencies coming from the sides or from the back of the microphone, by way of adding ports. These mics are called "directional" or "cardioid" microphones. Therefore, there would seem to be some real plausability to this myth. You'd probably need to carefully tune the mouth opening and turn your head in just the right direction, etc.. The effect is limited to sounds coming from certain directions, and the wavelengths affected are limited. Rifle muzzle blasts cover a very wide spectrum at ear-damaging levels.
Stand behind the rifle, wear ear protection, and you'll not have to think about it.