As explained here, relative that may only be employed to head restrictive relative clauses, while the wh- relatives may be used with both restrictive and non-restrictive clauses.
Early in the 20th century the Fowler brothers suggested a “division of labor” between relative that and the wh- relatives: that that should be employed exclusively with restrictive clauses, and the wh- relatives exclusively with non-restrictive clauses. The Fowlers acknowledged that no such distinction was observed in use; but the suggestion was adopted by the authors of many influential style guides, who attempted to elevate it into a fixed “rule”.
In consequence, there are many quite literate people who believe that this is a rule, and who follow it in their own work. That, I have no doubt, is the source of your discomfort with the use of wh- relatives in restrictive clauses.
There are, however, just as many writers who do not follow this prescription, and the T/W question is to this day a running controversy among people who care about such things.
I myself follow a practice just the opposite of the Fowlers' proposal—I use wh- relatives in all contexts and almost never use that as a relative in any context, for reasons which I explain here.
But as I say in my answer to the question linked at the top of this post,
that’s my choice. You’re free to follow your own rule, as long as you don’t put that at the head of a non-restrictive clause.
So we can’t give you a definitive answer. It’s something you’ll have to work out with your co-author.