Can this be made milk-free? Butter and eggs okay

If you're set on this recipe, you could try thinning out non-dairy yogurt with non-dairy milk till it's the consistency of buttermilk, which would preserve the acidity.

Hi! The buttermilk makes a difference in this recipe, but here's another yellow cake that uses white wine (!) instead: https://food52.com/recipes/6857-grown-up-birthday-cake