For what it is worth --
The general concensus on this and other Toyota-related boards is that the rear diff breather is essentially a one-way valve that, over the time of heat and cool cycles, creates a bit of vacuum in the housing. My question would be "why has Toyota done this?" Since even Toyota won't know the answer unless you are asking an engineer, let's guess:
Toyota, just as with all other vehicle manufacturers, build vehicles for street use. (Rhetorical Question Follows) In street mode, which would be the better situation: A) a fully vented axle housing that, without an adequate filter and a condensation trap, will allow contaminated air to pass into the housing; or B) leak-free seals?
Obviously, a leak-free housing is way better than having atmospheric air in the housing on a routine basis. Even allowing nothing but filtered air to pass back and forth into the housing will allow water to enter because air carries water all the time. Depending on where you live, it can carry a whole lot of water, and water itself can carry other contaminates such as salt. So, in a vented axle hot moist air enters the housing as it cools, and the moisture condenses on the housing. Reheating the housing drives the moisture back into the air in the housing, but does not drive it entirely out of the housing. Over time, your housing accumulates water condensed from the atmosphere. Not a lot, but enough to cause little puddles which will corrode housing and gears in time.
Alternatively, if you place a one-way valve on the housing, air passes out, but can't get back in, creating a small vacuum. Is this a problem in street mode? No. The vacuum is not great, and has little more effect than keeping oil from weeping past seals. It is not a strong enough vacuum to draw air into the housing (or it would not hold a vacuum) so it is not drawing air, water, or anything else into the housing. If air (which is a thin liquid) can not get in, neither can water which, in its liquid state, is far thicker than air.
So, from a street perspective, the one-way valve is the way to go. It keeps the housing clean and, by having a tiny vacuum at the inner surface of the seal, keeps the seals from weeping. No weepage, no customer complaints.
But on the street, heat and cool cycles are generally of long duration, and we rarely park our vehicles with the axles under water. It is not likely that you can often plunge cool an axle while driving on streets. Even deep puddle splash has little effect on the temperature of an axle because of the enormous thermal mass involved, the relatively low conductivity of the housing, and the short duration of exposure.
On the trails, however, we do see occasional deep water which, crossed at slow speeds, can tend to chill the housing at least sufficiently to reverse the flow of pressure through the check valve. The question is, can this sudden chill cause axles to leak water?
Probably not, as long as the valve and seals are in good condition. Whether the housing chills fast or slow, the differential in pressure is the same. If the housing is air tight enough to hold vacuum overnight sitting at home, it is sufficiently tight to hold vacuum while driving on the trail, all else being equal. So it does not matter whether the axle is rapidly chilled while crossing a water hole? It is no more likely to leak that way an any other. As long as everything else is equal and the seals are good.
Why then do we raise the vent? In my opinion, it is only to prevent untoward possibilities. If the one way valve fails and is also under water, water intrudes immediately. If the seals have gathered some grit that might possibly hold a seal lip open a bit and a chill occurs, water intrudes immediately. If your vehicle is bouncing back and forth over rocks, and the motion causes seals to be momentarily challenged due to deflection, and they are also under water, water can intrude immediately. If the axle housing is vented to atmosphere without a check valve and any of the above happen, the pressure is neutral at the seals and water is not likely to intrude. So, for off road use we use an atmospheric vent instead of a check valve.
Whether you use the stock check valve or a filter is up to you. I would suggest that if you are not doing hard core mud bogging or see deep water on a regular basis, extending the stock valve is probably a better solution because it maintains the factory intended environment most of the time, whereas using an open filter is going to allow atmospheric water to enter your housing every day. If you drive a dedicated off road vehicle, I would suggest an open vent, because it saves the housing in extreme circumstances, and we tend to maintain our axle fluids far more often than the average street driver would. In either case, I would extend the vent to a reasonably high position on the vehicle where it is away from splash.