Asuming they're reporting the pearson's correlation coefficients and not the slope of some linear fit (which they seem to use elsewhere) then a correlation coefficient with an absolute value <0.5 only explains <25% of the variation. Now that isn't actually too bad for a psychological test, so the fact that resilience and loneliness have are related to cognitive distortions is reasonable (and not too dubious a claim).
The main problem I have with it is that their main claim "Cognitive distortions predict safetyism" is based on a correlation coefficient of 0.25, this leaves roughly 90% of the variance unexplained which really stretches the meaning of the word "predicts" in their title. Also I don't have enough trust in their questionnaires to be sure that all of the variance in their results is actually directly caused by the thing they claim to be measuring so when you find some correlations it's hard to rule out it isn't caused by some confounding variable.
All in all someone's Cognitive distortion score is a pretty bad predictor of their adherence to safetyism belief. There's a nonzero amount of correlation between the results of their questionnaires but given the small effect size I'm dubious about their claim of a causal link between them.
I should at this point note that "percentage of variance unexplained" is a bit of a simplification and only really works for linear fits, but I'm using it here as a rule of thumb to reason about the strength of the correlation.