Not all insulation handles moisture the same. Some are inherently water-resistant, while others absorb water. Some allow water to filter or run through them, while others do not.
Water is going to affect your insulation, but being wet isn’t necessarily a catastrophic problem. How well it recovers can differ based on a number of factors.
Damp insulation can still insulate if some of the layers remain dry. But wet insulation can’t function properly as water is a conductor of heat. It also causes insulation to clump and compress, further inhibiting its function. Loose-fill insulation is more susceptible than batt. Spray foam is least affected.
Damp Insulation Is Better Than Nothing
While wet insulation is not nearly as good as dry insulation, it is still better than nothing—up to a point.
If the insulation is not wet all the way through, then some parts of it are still acting in the way that they are designed to.

If it is soaked all the way through, however, it is not likely to be effective since water is a good conductor of heat. It can prevent the passage of heat-carrying air, which may still make it relatively effective.
So, from a purely efficiency standpoint, damp or even wet insulation is better than nothing, but there are some other problems that might arise from the moisture (mold, wall damage, bacteria, etc.).
Moisture Compromises Insulation Effectiveness
Moisture inhibits insulation’s effectiveness because it occupies the air pockets that are between the fibers and because water is a conductor.
Insulation is made from materials that are naturally resistant to conductive heat transfer, i.e., the transfer that comes from contact. This means that when heat comes into contact will your wall; it will not pass through to the inside or outside (season dependent) because it can’t get through the insulation.
Now, air can often still pass through the insulation. If it is carrying heat, then heat can also pass through. To counter this, there are often spaces in the insulation that trap pockets of air.
When insulation gets wet, it compromises these functions.
If the material soaks up water and/or the water fills the spaces between the material particles or pieces, it soaks up and is filled with an extremely conductive substance, which will readily pass the heat through conduction.
Moisture can also cause the insulation to clump together and compress. This eliminates any spaces that may still have trapped warm air and also causes some parts of the wall, floor, ceiling, etc., to be exposed and not insulated at all.
Wet insulation can lose around 40-50% of its efficiency when wet.
However, this value varies depending on the type of insulation (which will be discussed next). Wet insulation (depending on a variety of factors) can also be dried in order to restore its effectiveness and efficiency.
What Type Is Most Susceptible?
Loose-fill insulations, like cellulose, fiberglass, and rock wool, are the most susceptible and the most greatly impacted by moisture. This is because they are less dense and have more air pockets.

As such, moisture has an easier time permeating through the entire thickness of the insulation as opposed to just affecting the outer layers.
Such insulation is also more likely to become compressed or clumped because of how fine the individual pieces or fibers are that comprise the insulation (a feature that makes the insulation less dense).
All that being said, rock wool does have the best ability to dry, so while it is easily made damp and wet, it can be dried fairly reliably and easily.
Dense insulation is better at resisting moisture because it is more difficult for the droplets to gain access to the insulation and to find spaces to occupy because these spaces are smaller.
While denser insulation is better at resisting moisture, once made wet, it is more difficult to dry because it is denser. Insulation in batts characterizes this category.
Water resistance is typically determined by the density and not the material. Insulations of the same material, for example, fiberglass, will be more moisture-resistant in batt form but will be more difficult to dry than its loose-fill counterpart.
Spray foam insulation is one of the most water-resistant, but it can still be degraded if water is allowed to remain on it for long periods.
This is to say that if it is suspected that the spray foam insulation is encountering moisture, it is important to remove the water from its surface so that the insulation isn’t compromised.
Even if wet insulation was still insulating, it poses health risks.
Sources
https://myenergymonster.com/ma/can-insulation-get-wet/
https://energyattic.com/does-wet-insulation-need-to-be-replaced/#h-fiberglass-batts