Changing monster's type and BAB / HD

[Pavlovian]

If I apply a template to a monster, to make an undead fey, and it specifically says:
- change HD to 'd8' (from d6 fey HD)
- change type to 'undead' (from fey type)

Do I leave the BAB from racial HD as is, because it doesn't specifically mentions it?

Or do I change it because if I look up the rules for 'Undead' it says it has another BAB progression?

[Wheldrake]

If you're the DM, you can give it any BAB progression you want.

If you're hell-bent on following the rules for monster creation, your critter would be treated as undead type for all purposes, including BAB.

But why limit yourself in this way?

[Lady-J]

bab is based on hit die, so ya if you change hit die you generally change bab aswell, however some templates while changing type do not effect bab or hit die