Race is a biological category, even if, like anything else, there are exaggerations and largely inaccurate stereotypes associated with it. And yes, it's more than just skin-deep, people, like all other living things, are holistic beings--not modular like human constructions--and as such all traits are interconnected, so there's no reason that differences in physical traits wouldn't correlate with differences in mental traits.

Lineages and hence genetics of different races are different, and we know that genetics determines mental traits because otherwise all different species of animals would think and act the same. Race isn't speciation, of course, but it's a lesser degree of the same principle, so there are mostly the same kinds of differences (other than the fact that different species generally can't interbreed, of course), but they're smaller.

It never ceases to amaze me the mental gymnastics that people somehow go through in order to deny what's plainly obvious. If race were merely a social construct, or arbitrary classification of a continuum of differences in traits, then you wouldn't see groups of traits commonly appearing together, such as blacks generally having not only dark skin but wide noses, always having black and frizzy hair, etc.

The fact that different races (or let's say "looks", in order to avoid begging the question) come from different parts of the world is also very telling because it indicates genetic divergence, and that would likely result in specific veins of differentiation, rather than there magically being a continuum of traits in between groups of people that were historically isolated, just like there is in the taxonomical tree of life.

I don't know if it seems like I'm invoking a straw man by saying that there isn't just a continuous spectrum of differences in all dimensions in which people tends to vary, but if there isn't, then there are discrete clumps of inter-correlating traits that diverge from each other, and that's precisely what the term "race" is describing (whether it's implied to be only skin deep or not), so..

If race doesn't exist, how do genealogists take a sample of someone's DNA and determine that they're, e.g., 99% Irish? Did they just make all that up? All the science behind the classification structure and placing the individual was just pulled out of thin air by scientists in the field, for the fun of it?

Also the argument that there's more variation between individuals of the same race than there is between different races doesn't hold much water, because even if that's true (which I haven't yet been convinced of), the significance of race lies in the specific types of variations that are associated with race, and those specific types of variations don't vary among a given populace (except where immigration, migration, interracial breeding, etc. have happened, of course). Also the differences that run along race lines happen to be very visually striking (such as being literally a matter of black vs. white, for example), and that's significant in itself and shouldn't be marginalized because there's no reason race can't be considered a largely aesthetic or visual property of humans. (If it seems contradictory that I'm saying it's largely visual and also saying that there are mental differences between races, it's not: I used the term "largely," and also my main point is that race exists, and some of my arguments are to that effect only. Race doesn't have to correlate with personality differences for it to be race.)

The argument that different races have the vast majority of their DNA in common doesn't hold water either, because it's obviously a little bit of the DNA that makes a huge difference. Humans have 99% of DNA in common with chimps and 50% of our DNA in common with bananas.

Political correctness is the force behind people denying that race exists, or just denying that race entails any differences beyond the physical, and nature is under no obligation to be politically correct and cater to our trending sensitivities.