In other words, let's say that two people have a higher-than-average number and size of homozygous blocks. How do we differentiate between the cause being (1) that they both came from a population with relatively low X-DNA variability, versus (2) a recent common ancestor?
By context. One should always look at DNA test results in the context of geographic origin, ethnicity, and genealogy. We currently have little information about whether some populations have lower X-DNA variability than others, but we will someday. I know of one published study that looked at one X haploblock, and found that it was more variable in Africa than elsewhere. They did not report substantially different variability in that haploblock within the populations of other regions, but we really need a lot more data on that subject to get a good picture of X variability within populations.
Because of the pattern of X chromosome inheritance, X chromosome haploblocks are less likely to suffer from founder effects and bottle necks than Y chromosomes. I would expect to see fewer differences in X-DNA variability between populations than we have seen in Y-DNA variability, but time will tell.
If an East Asian and a European have a lot of shared homozygous blocks, does that mean the same thing (as far as time to their most recent shared X-DNA ancestor is concerned) as if a European compared with an African have the same number/size of homozygous blocks...or on a finer scale, if a Portugese person is being compared with an Irishman, compared to two other kinds of Europeans?
The concept of "time to their most recent shared X-DNA ancestor" seems problematic to me. When comparing two people's shared haplobocks, different haploblocks will have different most recent common ancestors who lived at different times.
When comparing a haploblock between two people, we might be able to get a general idea of when the most recent common ancestor lived by looking at STR differences within that haploblock, just as we do with Y chromosomes today. If a European and an African had matching haploblocks in their 23andMe results, I would expect to see more STR differences in that haploblock than if two Europeans had the same matching haploblock.
The other thing that occurs to me is that it could be important to consider is not just how many (or how large) the shared homozygous blocks are, but where they are located on the chromosome.
Absolutely. For example, a large haploblock that spans the centromere has different implications than another haploblock of the same size that doesn't span the centromere.