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This answer to Nature of “the silky black 'highly flame-resistant felt'” on Block 5 Falcon 9's, and its intended functions? contains the following:

This came into Falcon 9 design with Block 5 improvements. As Elon Musk mentioned in updates about Falcon 9 Block 5 it is carbon fiber hydrophobic thermal protection developed at SpaceX. The reasons why they replaced are pretty obvious. One reason is the heat factor and the other reason is expenses.

Question: Why would the Falcon 9 Block 5 carbon fiber thermal protection material need to be hydrophobic? Is this for its thermal properties, or purely aesthetic (stain-resistant?) or perhaps is this just an quirk of the way the material behaves and isn't for anything in particular? Might keeping it clean keeps the thermal emissivity high, or the visible reflectivity low (i.e. "looks cool")?

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    $\begingroup$ Is it to avoid icing prior to launch? $\endgroup$
    – Steve Linton
    Jul 6, 2020 at 8:35
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    $\begingroup$ Hydrophobic materials are sometimes referred to as ‘self-cleaning’. Teflon is the best known hydrophobic material. en.wikipedia.org/wiki/Self-cleaning_glass $\endgroup$
    – Anthony Stevens
    Jul 6, 2020 at 10:58
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    $\begingroup$ Non-hydrophobic materials tend to lose rigidity or tensile strength as they absorb water. This might be viewed as a bad thing. $\endgroup$
    – Carl Witthoft
    Jul 6, 2020 at 12:18
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    $\begingroup$ +1 to @SteveLinton, cryogenic temperatures pull a lot of water out of the Florida air and ice building up could cause problems, they wouldn't want ice to constrict the TVC on the engines. $\endgroup$
    – Dragongeek
    Jul 6, 2020 at 13:59

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There are two considerations I would guess motivate the hydrophobic properties of the thermal protection system:

The first is protection against the wear of use to increase the lifetime of the material. Falcon 9 encounters high exposure to water from the sea-journey return but also from the Merlin exhaust during re-entry and landing burns. The exhaust of RP-1/LOX at their mixture ratio is roughly 25 percent water by mass. As mentioned by Carl in the comments, absorbing water from either of these sources would affect the strength of a normal coating.

The second is, as you mentioned, the thermal properties. The primary heat load on Falcon 9 is convection from the atmosphere and its own exhaust. The convective heat transfer coefficient is related to the Reynolds's number of the flow (through the Nusselt Number) and therefore positively correlated with density. A hydrophobic coating would limit the interaction between water molecules and the surface, effectively lowering the density of the flow considered for heat transfer and reducing the ultimate heat load.

I have no source to show that these are the motivations behind SpaceX's decisions, but regardless they are both very useful consequences of their design.

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