This is a very thoughtful proposal to use existing longitudinal data to address the question of whether climate change concern affects mental health measured at a later time.  This will contribute very usefully to the ongoing debate whether concerns or anxiety about climate change occur in individuals who are already suffering from ill mental health, or whether they cause or exacerbate mental health problems, or both.  

As the data have already been collected and it is not possible to change any aspect of the study except the planned analyses, this is a somewhat unusual registered report. If given the possibility, for example, I would have advised the authors to measure climate change concern also at T2, and to include other, validated measures of climate anxiety to assess validity.  Given that this is not possible, I only have one suggestion about the analyses, and a few about the write-up – overall, I very much think this study should go ahead and be executed as planned, even though the available data cannot answer all the questions we may have on this topic. I also don't have state-of-the-art expertise on all the analyses proposed, esp regarding treatment of missing data and the interpretation of the resultant findings.

Throughout the manuscript (including figures and figure captions), I would suggest to change the phrasing of “… cause mental health”. From my perspective, if you use the term “cause”, then you would need to refer to a specific outcome (e.g., good mental health, mental health struggles).  If you want to keep the directionality or valence open and simply refer to the domain (i.e., mental health), you might need to use a different term such as “affect” (e.g., “… affect mental health”).

For the final article, I would also advise including more subheadings to provide a clearer structure and overview for the reader, especially in the “Exposures” and “Analyses” sections.  Related, the term “exposures” is unfamiliar to me in this context, could this section also be named “Measures”?

Finally, I would suggest including the variable of “having children” as an additional potential confounder (I assume this is available in the data).  This life change may trigger new or increased worries about the future, but can also affect relationships and mental health especially in the perinatal period, so it would seem useful to control for this, especially in the age group available for the study.