Well the physical aaspect does come in to play for every single human being alive...there simple will be NO relationship on either side if there isn't some physical attraction. Not drop dead...but something.
Mental, yes she does have to be able to hold an intellegent conversation, because despite what you might read here I do as well.
Spiritual, she can worhip trees for all I care as long as she doesnt try to force religion on to me.