Jerry -
This isn't an old thread so don't worry about it. Besides I like to see some old threads come up since they're generally interesting.
I'm sorry but I'm not savvy at all with making Castile or Bastile. I can tell you what I did which you might find helpful. I've never made "Castile" because I've always added something to the olive oil like a dairy item or some coconut and castor. So, I make only Bastile batches. I've never had a snow white batch. The buttermilk was the lightest in color and it was still cream colored. I know using refined grade A olive helps with keeping soap 'whiter". Also freezing the milk and adding the lye very, very slowly so the milk doesn't change color and not letting the batch gel. This is what I did with the buttermilk Castile - just refined olive, frozen milk and stuck it into the frig. Normally, I use enough water for the lye and use dairy for the rest of the liquid to keep a batch lighter in color. You probably need to add titanium dioxide to the batch to make sure it stays white since mine still came out cream colored. I can't give you advice on TD since I haven't used it for several years. I don't know why. I've got some but I just don't use it. But there have been discussions about TD in which people have mentioned how much they use.
Since I'm not too particular about color change, I've never really worried about keeping dairy as cool as possible. A long time ago, someone posted a picture of soap she had made in which she used coconut milk and TD. The soap was white. It was beautiful and it looked like a frosted cake. However, I don't remember if she mentioned the oils she used in it. I wish I remembered who posted it because I couldn't find it and a username would have helped narrow the search. Maybe I didn't even see it on this forum
Anyway, you might find coconut milk will produce a 'whiter' batch than dairy. I don't know if it will but it's worth trying.
Some FOs I've used which haven't discolored are Peak's Love Spell and Black Raspberry Vanilla. But again, I wasn't trying to achieve a white soap and was very happy with the cream color of the portion in which I didn't use colorant. You could browse through the
FO Spreadsheet and see which FOs haven't discolored. I really like Peak's Blackberry Sage and I haven't found it to discolor but I don't think I've used it in a milk batch. Surprisingly, Blackberry Sage is well liked by everyone who's sniffed it. Usually, someone always dislikes the scent of a batch or at least is indifferent to the fragrance.
I hope you found this a little helpful and maybe someone else will have better advice.
). I don't know if you can tell below but the lather was nice. Smaller bubbles but quite a bit of them. I was able to get even more of a lather once I put the camera down and used both hands. Also, it lathered better in warm water than in cold. I wish I could have answered your question but I just don't remember. However, I can recommend olive with milk because it has a better lather than Castile (IMO) and it's really gentle. If you make a batch soon, you'll still have at least 6 months which might be enough time for Christmas. 
