I am looking at an application that was taken face to face and the applicant did not wish to furnish the information. The LO marked their Ethnicity as Hispanic but did not mark their race. Do we leave that blank?

The LO should have made a visual observation. I would send it back to the LO to get this information.

Correct. The loan officer has to get all 3 (ethnicity, race, sex) on all applicants that are in person.

How do you determine their race when they are Hispanic because they could be of many races? Do we assume they are white??

Do they look white? Do they look Native American (most Mexicans and many other Latin Americans are a Native American/Spanish i.e. "white" mix)? Do they look black?

Here's just an example of the array of races that can be exhibited within the "Hispanic" world (I haven't researched their racial backgrounds, but here is how i would classify them if i had to on visual observation):

Pele (great soccer star of the past): black

Sergio Garcia (current star golfer): white

Julio Cesar Chavez (former boxing champion): white, Native American

Jorge Chavez (former horse racing jockey): Native American

(I used at least semi-famous people so you could google them if you wish.)

The point is, all of them are "Hispanic", but they are all racially quite different.

This question prompts me to ask if borrowers really opt not to provide the information frequently.
We only get this issue every once in a great while now that repeated training has emphasized the LO MUST ask, not just assume and mark YES x3.