Hello!

Undead in D&D are immune to fear (unless they get turned, or exorcised,or something). However, there is sentient undead, which is undead who are capable of complicated thinking (ghosts, vampires, and liches, to name a few). Do you think the phobias they had in life would still affect them in their new form?

As long as we treat phobias as character traits, then yes. But thinking like an undead, they would have a perspective on life and death that they didn't have before, and true paralysing fear would likely evaporate in a combat situation due to their newly enlightened perspective. So a vampire afraid of spiders may suddenly find himself laughing at a giant spider once his brain has broken it down to its living parts and he realizes that it is realistically little to no threat to him.

The thought of being teleported to a sunny beach would probably terrifying to a vampire. It depends how much the GM spend time fleshing the character out and on the RP intensity. The rule with the fear immunity is IMO merely there for the fear type spells.

Hmmm i guess it depends on how much of their original personality remains.

Also depends on if they are governed by emotions or not (after changing). I would think most undead don't feel anything emotional, and large portions of the psyche would have been ripped away with their humanity. And possibly new senses may give them a new perspective of which seeing a 'spider' may look more like a snowflake or the phobia reassigned to something more relevant to the new existence.

I suppose the weaker the animating magic that created them the more likely (the original) phobias would have survived, and early on. But eventually instinct and the dark magic animating them would override it all.

But having silly phobias would still be interesting for a player; Say a vampire afraid of blood or the darkness, a ghost afraid of other ghosts or of anything he can't touch.... ummm... i can't think of any others that make sense...