Yes, social media stats are trustworthy. Social media is an exceptionally democratic platform that can be used to get a good idea of public sentiment regarding issues of various importance. For example, there was a great deal of excitement on social media for Donald Trump and very little for Hillary Clinton, who lost the election.
These kinds of "personality tests" are often fake and false. They might be fun, but they don't really have any real gauge of someone's personality. Real personality tests are much longer and ask much less leading questions, and even they are not accurate enough to be considered a scientific test.
The spinning dancer optical illusion does not tell anyone a great deal about their personality, other than the fact that they tend to privilege one hand over the other and that it can affect their perception. This is neither profound knowledge and nor does it tell anyone anything useful about their personality. While these studies might be serious and academic in origin, social media often distorts them entirely.
There is a word for the things that appear on the Internet. It is called click bait. People will post whatever they think people will click on. That allows the epople who run these websites to make money off of ad clicks and other things. There is no concern for whether the information is true.