Hi Ducky1,
There is more information about the tradeoffs involved in different types of mattress protectors (and by extension mattress encasements which I generally don’t suggest unless there is a specific need that indicates it) in post #89 here.
The “membrane” type protectors or covers are generally less breathable than other types because being waterproof they only allow water vapor to pass through which can reduce ventilation compared to other types of cover. This reduction of ventilation in a mattress would be even more with an encasement than with just a protector that covered the surface of the mattress. Of course for many people the tradeoff between waterproof qualities (vs water resistant or just moisture absorbing) is worth it because you won’t have every benefit to the same degree in a single product.
Some of the cotton encasements which have smaller pore sizes such as these can also be an effective allergen barrier against dust mites and are more breathable but these are not waterproof.
Post #2 here may also be worth reading if dust mites are your biggest reason for choosing an encasement over a protector.
Everything is a matter of which of the tradeoffs involved in every choice are most important to you because you won’t find a single protector or encasement which has every property to the maximum degree where there are no tradeoffs involved.
Phoenix
PS: I deleted other other thread which was a duplicate