Well it is wrong to say that people with Down syndrome look alike, but they do have a similar aesthetics. Down syndrome is what happens when the baby is born with 3 copies of chromosomes 21, instead of 2. Having 3 copies of the chromosomes 21 lead to the change in the body, including the unique facial shape and the developmental delay. This is a mutation that is most common that isn’t fatal, also known as Down syndrome. Everyone who has them has a severe mutation to their genetic code. So they have distinctive facial structures and malformation on the ears, hands, and feet, none of which looks the same.
It is our human tendency to see a pattern in things that doesn’t have one. While people with Down syndrome often share common features, almond-shaped eyes, flat face and round faces, they still look closer to their family than others with Down syndrome. It’s just our brain not used to seeing something that isn’t what it used to and then categorizes them in the same light. It’s the same reason why Caucasians might think that all Chinese looks the same, while the Chinese could easily point out which one of them is actually a Korean. There is totally nothing wrong with it, but the more you hang out with the group of people that you assume to look similar, the more you can differentiate them. This is the case for twins too. Their family members could easily tell which one of them is the older one while strangers couldn’t differentiate them at all. Since we don’t tend to hang out with people with this disability, we end up grouping the distinctive people with Down syndrome as one, just like how one looks at another race.