That's a weird study. The first thing to acknowledge is that this was not written by "scientists" but only one person. This person has a
webpage that includes statements that endorse (via Google Translate): "Wokeness does not seek compassion or empathy," "Wokeness opposes free speech," or "Wokeness raises a bitter lens to one's eyes." This is not exactly the most objective person to have conducting this type of research.
On top of that, the study approach is a bit of a circlejerk. His scale is based on individuals who agree with “If my friend called me ‘woke’ in good faith, I would agree with them, regardless of whether I approve of the term or not.” What does that mean? What is meant by "woke" here? It is clearly open to interpretation and provides no reliable definition of the populations he's trying to describe. By creating a vague statement, his entire analysis is solely calibrated on a poorly defined meaning. Furthermore, we all know self-reporting can be difficult when using a vague term. For example, if we changed his sentenced to "If my friend called me 'MAGA..." we all know there are many people who clearly endorse MAGA philosophy but refuse to acknowledge they are true believers of MAGA. This is perfectly encapsulated by certain posters here who love to post MAGA beliefs but then try to pretend they aren't actually MAGA. This study runs into the same problem on the other side of the spectrum, which creates major reliability issues.
The final weird thing is his central analysis. He uses a numerical score from his scale and compares it to values representing anxiety, depression, etc. A competent data analyst would recognize you have two numerical values (just ignore for a moment his scale is ordinal) that the best way to analyze the data would be a regression. Except he doesn't do that. He takes his scale and divides it into two to create two separate groups. One is the high scoring group, the other is the low scoring group. This would make sense if his scale was bimodal, one peak in the high and the other in the low group. What if it is a simple bell curve? Dividing it in half looks very suspicious. Imagine if someone did a survey about legalization of drugs. You'll get generally three opinions: 1) All drugs should be legal 2) Some drugs should be legal 3) All drugs should be illegal. What the author of the study would be ok doing is taking the data from those who believe "some drugs should be legal," dividing it in half, and lumping half with legalize all drugs, and the rest with banning all drugs.
He provides zero rationale for performing such an odd analysis. I suspect its either incompetence or he is purposing mining the data to get the result he wants. There's a reason that this is published in the Scandinavian Journal of Psychology and n
ot in the ~100 or so psychology journals considered to have higher prestige.