If this is indeed related to standard authorization checks, wouldn't running authorization trace provide hints on what is missing?
If the authorizations are completely identical and this problem occurs only for some users, while the rest have no problems displaying the same documents, I would suspect some custom code, which checks for example assignments in a z-table or based on organizational data.
Did you try checking out your project documentation or recently imported transport requests? If there was indeed some development it would be (hopefully) documented somewhere...
In your first screenshot you have entered no customer and no materials, while on the second one you show a screenshot of some item with a certain material, which looks a bit confusing.
From the create sales order screen it looks as if there is some variant applied. This can be done for example via a separate tcode or via a variant assigned to the document type.
When you compared the behavior between users at order creation stage - did you ensure that users execute the same transaction code and use the same document type?
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