All names are referencing MCP mappings.
In the class Pillager Entity the updateEquipmentIfNeeded method checks if the item is an instanceof BannerItem, else it then checks if via func_213672_b is a Items.WHITE_BANNER which is an instanceof BannerItem, but due to the initial if statement it would prevent the statement from ever being true.

Mojang names are:

• Pillager.pickUpItem(ItemEntity): Which already checks instanceof BannerItem
• Pillager.wantsItem(Item): Which checks for the white banner