The question asks:
Can Mormons really distinguish other Mormons from non-Mormons based on skin texture?
That is a reasonable question given the quoted Digital Universe article says:
A study done by psychology professor Nicholas Rule, of Toronto University, shows that Mormons and non-Mormons alike can identify Mormons based on no more than their skin quality.
However, this is not what the original 2010 PLOS ONE Article claims.
The article is about the ability of participants to detect whether faces (carefully selected from an online dating site) were of Mormons or non-Mormons, and what factors might be in play.
The first issue is they did not test the skills of Mormons at this task. They only tested the skill of non-Mormons!
Twenty-three undergraduates (n = 19 females) categorized each of the faces as Mormon or non-Mormon in exchange for partial course credit; none of the participants was Mormon for any of the studies reported in this work.
Later they report this as a limitation of the study:
As our participants expressed very low levels of exposure to Mormons or Mormon culture, it is very interesting that they were still capable of distinguishing Mormons from non-Mormons. Because Mormons have been found to be more accurate in categorizing members of the two groups , it is possible that the present data provide more conservative estimates of the strength of these effects. It would therefore be interesting to investigate these same effects among Mormon perceivers.
Already we can dismiss the claim in the question. Well, we can't say it is definitely false, but merely that no evidence has been presented to support it.
Next, there is the question of whether the (non-Mormon) participants are accurate at distinguishing Mormons at all.
In Study 1, given "full" photos (i.e. a cropped headshot, showing only Caucasians, without earring, tattoos or other adornments that might disqualify them as Mormons), they participants had a mean accuracy of 0.56. This is (significantly) better than chance, but highly unreliable.
Although the mean rate of accuracy observed here was relatively low, it is on par with the effects reported for other nonverbal facial cues, such as rates of accuracy in categorizing certain facial expressions of emotion
It barely counts as "being able to distinguish" as suggested by the question.
Finally, the question is worded as though skin texture alone was enough to determine whether the picture was of a Mormon. The study did not claim this. It only claimed it was a single factor. A single factor isn't enough (e.g. when I see a paper was published in PLOS ONE, it is a factor towards me distrusting the science, but it isn't sufficient!).
They argue that Mormons are generally healthier (They explain that this likely due to their substance-free lifestyles, routine health behaviour, early marriage, regular church-attendance - but they also allow that some Mormons attribute this to divine influence.) They hypothesize that the participants subconciously use this to influence their guesses. They also hypothesize that skin texture is one of the factors that is used to perceive the health of the subjects in the photos.
So they had the photos rated by skin smoothness, and showed how this correlated to how the final decision was made.
But although perceivers could categorize the Mormons and non-Mormons significantly more accurately than chance, they appeared relatively unaware of their ability to do so. Information about health from the faces seemed to form the basis for perceivers' categorizations of Mormon/non-Mormon group membership, with facial skin quality serving as the primary cue distinguishing the two groups.
In summary, the report's findings were mangled by the journalist who wrote the quoted Digital Universe article. It may or may not be true that Mormons can distinguish other Mormons from non-Mormons based on skin texture, but, as of 2010, there was no scientific evidence of it.