Why are a lot of liberals seemingly opposed to talking about differences between groups of people, especially when the differences involve things that are important? I’ve found that class, racial/ethnic groups, and crime rates seems taboo to them.

Because these "group differences" people identify are usually class differences in disguise, and they are used to oppress people, by consigning them to different positions of power in a society. This is what makes them dangerous. This is what Marx identified--- the class structure in society--- and if you are blind to it, you will fall prey to adjusting your sense of people's worth using small class markers that will then cause you to discriminate. If you are aware of class, you very quickly realize that every single one of the group differences people identify are class differences, and have nothing to do with anything else.

Look, there are racial generalizations that are probably not so offensive to people: "Black people often like to raucously contradict each other in public! They'll argue loudly in front of others. White people will never tell you you are wrong, even when they know you are full of shit." That's a pretty normal overgeneralization, it's not particularly offensive, it would probably be used by a comedian as the basis for a comedy routine. It was vaguely statistically true, at least in college, I know people in the US would say "Oh! So true!" When they hear this.

But secretly, even this little social thing is a class marker. Arguing loudly will cost you social status, by creating political opposition, even though it allows the group to be more precise and accurate in thinking, because the ideas are debated. So what you are saying is simply that you see more politically careful white folks, that political care is culturally embedded in the American white society, at least among Northern Europeans and British folks, not so much among southern Europeans or Jews. Jewish culture is sometimes even more argumentative than African American culture.

Similarly, "white people listen to music that is so cold and dry. Black people listen to music that has a lot more emotion". This is also kind of true as an overgeneralization, but there is a real important cultural tradition involved: Europe has a very strong and unique (and extraordinary) written music tradition, which is very developed, and extremely important to preserve, and it sits there in the subconscious of people with European ancestry. This written music tradition is rhythmically dead, because they couldn't write down rhythm well, the notation is totally inadequate. When you do, it's extremely difficult to annotate syncopated rhythms, or weird off-beats, or polyrhythms, the notation fails completely. So European music from before 1920 or so, before jazz and contemporary classical music developed, tends to be in a very monotonous rhythm that is suitable only for a limited range of emotions, mainly bombastic grandeur like Wagner, or weird intellectual note-pattern noodling stuff like Beethoven's string quartets, it's not natural for coming up with zany stuff like a Samba. The great classics generally alternate noodle-bombast-noodle with bombast-noodle-bombast like the Pixies. I like note-pattern noodling, but the main effect on the brain is to produce a tonic-analysis, and various shifts in internal grammars for giving the music structure, it does not produce a wicked desire to get up and dance.

In Africa, there is a tradition of improvizational polyrhythmic drumming, and this was very developed, more so than anywhere else. The polyrhythms and general rhythmic awareness is far more developed than in Europe, precisely because the music is not written down, and it is mainly a percussion tradition, not the greek analysis of harmonic note progressions and tonic resolution.

But a racial person will then use this to distinguish then between "sun people" and "ice people", and offensively claim that Europeans can't dance or drum naturally, or do polyrhythms, or that Africans can't learn to write down interesting note-progressions! This is mentally deranged.

I have chosen less offensive examples, but this one is the worst.

The 20th century saw a bunch of people take a bunch of trite puzzles, and compile them into a puzzle-solving test that they called "IQ". The point here was to consign people who were not particularly good at solving these puzzles permanently into menial labor castes. They carefully made means and statistics to ensure that IQ would center at 100, with a standard deviation of 15, and that men would score equal to women on average (by recentering the puzzles using weighted averages of baskets where women did better and ones where men did better on average).

Anyone can easily learn to solve these puzzles, it's much easier than learning any real skill. Generally, in certain cultures, you are exposed to similar puzzles early and often, for example, I was given various mathematical puzzles by my father at age 3-4. The key distinguishing feature is the embedded mathematics in the culture, whether there is a rich mathematical tradition that is transmitted by people to their children.

The reason this test was developed was to institutionalize class differences between people based on a biological notion of racially-inherited intelligence. When the test was developed, former slaves scored on averege about 2 sigma lower on the tests than the slave-masters and their children, and immigrants from southern Europe similarly lower, and so on. That was very good for the racists, they were happy they had an objective sounding method to justify the power-differences.

People didn't view this puzzle-gap as a spur for former slaves to learn to solve puzzles, but as a sign that people from certain part of the world have inferior brains. There is nothing inferior about anybody's brain, puzzles are not hard. Everyone can and should learn to solve those stupid puzzles. They aren't completely trivial, and you need to sit down and sort out various small things before you do well. These things you sort out then allow you to learn mathematics more easily.

But the goal of these tests was to discriminate, and discriminate they did, they still do, although by now, a century later, the difference between races is less than half a sigma, and the whole test performance by people in general has increased by more than 2 sigma as compared to when the tests were first created, simply due to the exposure people have to the puzzles involved.

So, in general, it is very good that people are hostile to talking about "differences between groups". It's because anyone who talks about these differences is creating a situation to institutionalize class difference and prevent a classless society, and should be marginalized and heckled and dismissed, because they are lying for nefarious social ends.