Issue with editing vertices

In essence, I don’t know if this is a feature, a technical issue, or what, but this is the problem I’m having:
In one particular section of the model I’m working on, it seems that all movement of the vertices are locked to the green axis. I can only move them in relation to this axis, no matter what I try to do. I am not holding shift down to lock the inference, and no matter what I try to do, I cannot change it.
This has frustrated me to tears, and for all I know it could be my fault, but I can’t find any information as to what could be causing this, or indication in SketchUp that tells me what could be causing this issue.

Please, if there’s anything I can do to fix this, I would appreciate the help.

Moving vertices is something you can only do at times wihen having nothing (else but the move tool) selected prior to hovering over these vertices with the ‘Move’ cursor.
So your question and following text is a bit confusing as to what you are actually doing.

Do you know that you can constrain to other axes with the [Arrow] keys instead of holding down [Shift]? [Left] is for green (not your choice here), [Up] is for blue and [Right] is for selecting the red axis.

If you are trying to move a ‘Glue To’ group or component (glued on a green/blue face) then right click on it and select ‘Unglue’ in the context menu.

Maybe you just need to orbit to view in a direction not so much along green.

Could you elaborate on the steps you do and what exactly you are trying to move?

Move Tool: Moving or stretching with Autofold
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Thank you very much for the help, Geo, that seems to have been the issue.