I am in the cold water camp. I use cold water and Ivory soap (the bar). Soap in cold water and then on a hard flat surface rub it with the Ivory soap. I generally use my fingernails (If I know whose blood it is), or a old plastic card, such as a credit card and rub back and forth. I have used this technique for years and it works. It works well for period leaks too.
If the fabrics cannot take scrubbing, then I would check with your local museum about the best way to remove the stain without damaging the fabric.