No you are correct and I understand the confusion, this discrepancy is pretty common in literature and usually stem from varying interpretations based on the context, like different sample characteristics or research conditions (sample size or type of invariance tested). Also, different fields or even different reviewers accept slightly different thresholds. For instance, from one of the tables on rejection rates in Chen (2007) you can see that ΔCFI contains two sub-columns for the different sample sizes, ≤−.005 & ≤−.010 which represents two sensitivities, ΔCFI ≤ −.005 is a more lenient threshold while ΔCFI ≤ −.010 is stricter, it is up to you as a researcher if you want a really strict or a less strict cut-off

Hi Marius Ole Johansen , you know what confused me. If my indicators ΔCFI > -.005 or -.010 are correct in suggesting measurement invariance. Then what does that mean when the authors (as shown in the screenshot) used ΔCFI < -.010. Then some authors used ΔCFI < .005. How can it be that I used for instance > -.010, then they used < -.010? Someone must make an mistake.

In Chen 2007, the indicated ΔCFI < = -.005 or -.010 as non-invariance, which means > -.005 or -.010 as measurement invariance. Right?

I got some clues, Kline (2016) and some authors used absolute model fit change. Also I think one author might did a typo. If this was the case, then things make sense and the 17 articles I read basically used the similar indicators.

Kline, R. B. (2016). Principles and practice of structural equation modeling. Guilford Press.