I should also mention this recipe has a water discount (reduced amount of water – which helps the soap sets up faster in the mold) and is about a 2.35 : 1 water to lye ratio (which is a setting on the lye calculator). Using the standard full amount of water/liquid makes a softer soap that takes longer to firm up.

Hi Lenora! Yes, you can exactly halve and exactly double a recipe, if you don’t make changes to the oils.
You’re 100% correct that the smaller the recipe, the more careful you need to be about measurements since small changes have bigger effect in small recipes.
In this case, when I plug the recipe in a lye calculator (I used Soapee) to get the half batch amount, it says:
4.36 oz (124 g) water
1.86 oz (52.6 g) lye
13 oz (368 g) olive oil
1.5 oz (46 g) castor oil