Problem is the one way (check) valve. When your hot diff is submerged in cold water, the air inside it quickly cools causing a drop in air pressure. This sucks in water around the axle seals since the check valve closes.
Edit:
Here is article about it
Why You Need Diff Breathers
photo by Luka Banda via iStock A huge wave comes raging over your windscreen, your engine screaming, and your seat getting dirtier and dirtier – congrats, yowww.4wdtalk.com
The math states otherwise, the 1/4 steel axle housing will transfer the temperature change very rapidly, however both the oil and air inside the axle are excellent insulators and will cause the reaction a significant delay to cool those two volumes down(anywhere from 3-10 minutes). The math also states the pressure differential it could develop if instantaneous temperature transfer could occur from 250F to 33F at 5000' is <4 PSI and ~4 PSI at sea level. The higher the elevation the less differential it can develop. Since it's not going to rapidly cool the oil and air it doesn't pose the risk they want you to believe. Been there done that and nothing ever got into my axles, with the breather on the axle.
The bigger worry would be the axle shaft contracting due to the rapid temperature change, but rubber expands as its temperature decreases.
These simple breathers have been around forever and worked just fine; they do however require periodic maintenance.
The front is the one to be concerned with since water can lift the cap up when entering water too quickly, but even then it would likely be less than a few grams of water it would allow in before the water forced it to seal anyway.
If we are going to freak out about breathers lets mention the other style is open to the air allowing dirt into your diff at all times. To each there own but neither style is a concern to me.
