Why shore it's easy either way, repair or replace as you choose.

Yes ^^^^, looks like MDF and water damage from the shower.

It’s next to a shower. The shower isn’t “leaking,” but that area will sometimes be exposed to water splashes.

Is there a more water resistant baseboard material available to replace the old baseboard?

Why shore, pvc,vinyl, polyurethane, polystyrene and resin are more water resistant. Then of course there's Bois-d-arc , white oak and cypress if you need wood that is more water resistant.

jaxo: Denial is a river in Egypt and you're there. When you pull that baseboard to replace it, the framing behind will be black from mold. You aren't getting out of fixing your leak by replacing the cosmetic problem.

Which seems more likely, you're consistently splashing on the bottom and right side of the baseboard only, or the baseboard is sucking up water from the end and bottom from a leak?

^^^^^, yep, I agree with all of what Joseph said. That is not splashing, way to much damage.

Ever head it said "one picture is worth a thousand words"? Well this demonstrates how that works. Despite op repeatedly denying door leaks, the picture clearly tells us that someone certainly thought door was leaking. Note the gobs of fresh caulk. I hope all that caulk wasn't applied strictly for appearance.

All that is to say Joseph is right, cussing and discussing doesn't fix it. Time to get busy facing facts.

It has been like that for years and it hasn’t been wet recently. Maybe it got water on it years ago when there used to be a shower curtain before the glass enclosure was installed, or maybe a wet mop touching the baseboard caused damage when mopping the floor.

The caulk was added as a recommendation for pest control for insect exclusion.

That's more damage than a wet mop touching the baseboard would have done. Either the shower curtain was consistently allowing water to pool in that corner, either you still have a leak but the damage only gets progressively worse so you don't really notice it getting worse.

As others have pointed out, there is going to be black mold behind that basebaord, and the damage is too important to have been caused by only one isolated event.

No threshhold showers are a great idea. But unless someone is wheelchair bound, best to avoid.

I just got it replaced.

No mold. Whatever water was there a long time ago looks like it has been dry for years.

Not sure what the black material behind the drywall is. Looks like plastic, but I didn’t look at it closely. I just took a quick picture when the contractor stepped away.