If the block or item is not on the list below, then they cannot pick it up.

Enderman can pick up… :

• Cactus
• Clay
• Coarse Dirt
• Dirt
• Flowers (Short)
• Grass Block
• Gravel
• Melon
• Mushrooms
• Mycelium
• Netherrack (Java Edition Only)
• Podzol
• Pumpkins
• Red Sand
• Sand
• TNT

In the upcoming Nether Update (1.16) they’ll be able to pick up:

• Crimson Fungus
• Warped Fungus
• Crimson Roots
• Warped Roots

NOTE: In the upcoming Nether Update, Enderman will no longer be able to pick up Netherrack.