Oak bathroom wall cabinet – stylish storage or moisture magnet?

Any natural wood is porous to some degree, but the hardwoods contain a more complex lignins which makes them tougher and longer lasting. The issue with natural wood is if the moisture gets into the grain as it would in nature when the tree were alive. The way the fibres lay allows moisture to wick up in much the same way as it would transport nutrients when alive. If you look at fence posts, you'll see a capping piece on the top which is there to stop this from happening due to the way logs are cut.

But while any natural wood is fairly watertight up to a point (we used to make primitive boats out of it even before the discovery of tar as a sealant). Hence the phrase "No point spoiling the ship for a ha'peth [half a penny] of tar".

Man made composite boards can be very strong and waterproof if they are designed to be but most are not. The size of the particles makes a huge difference with HDF (generally) being the most resilient and the various chipboards generally being the weakest. Plywoods are, like natural wood (because they are natural wood) only really trouble when the grain end is exposed.

Man made boards are simply glued with a plastic like PVA which is a plastic that dissolves in water and large particles found in chipboards - which make up the vast majority of "contiboard" (plastic covered wood found in kitchen and even bathroom units) are largely made up of voids full of water-soluble adhesive.

Hydrophobic paints, properly applied, can seal pretty much anything from chipboard to mahogany, not that anyone in their right mind would paint something as beautiful as natural wood with white paint. Modern lacquers are very resilient with the stuff for outdoor uses generally being better because they are designed to withstand extreme temperatures, sunlight and driving rain.

Water will find its way into any gap and since the molecules are quite small, water is only held back by surface tension which is easily broken down by soaps - as you might find in a bathroom. Plasticised MDF panels - which make up the majority of kitchen units are well known for "blowing" (delamination) when water creeps in. So the answer, generally, is stick to natural wood and ideally, make sure it's properly coated.

https://forestplywood.com/blog/plywood-uses/mdf-vs-hdf-how-theyre-different-and-what-theyre-good-for/

Oak looks great but in a damp bathroom it really depends on the finish and how good the ventilation is. If it’s well sealed (oil or varnish) and you’ve got an extractor fan running, it holds up fine. MDF swells fast if it gets damp, so I’d lean oak if you can keep the moisture managed.